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Syllogisms Part 2
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Dodos aren’t always weak, but they are always zipzaps. Not all those that are zipzaps are weak, but they will be boings.
Explanation
- All those that are zipzaps are dodos
No. We are told that all dodos are zipzaps but we don’t know if the reverse is true.
- A weak dodo is a zipzap
Yes. We are told in the first sentence that all dodos are zipzaps, so a weak dodo is therefore also a zipzap.
- A weak animal cannot be a boing
No. We are not given any information in the question stem about animals so we cannot draw this conclusion from the passage.
- Some boings are dodos
Yes. We know that all dodos are zipzaps and that all zipzaps are boings, so dodos must be boings as well. Hence some boings will be dodos.
- More zipzaps are weak than boings
No. The last sentence tells us that more zipzaps are boings than are weak, because all zipzaps are boings but only some zipzaps are weak.
Shorthand method:
Not all D = W
All D = Z
Not all Z = W
All Z = B
All locals who like tea also like coffee. All the locals on the beach were German. No locals on the beach liked eggs. A few locals on the beach liked tea. All the locals on the beach liked photography.
Explanation
- All Germans like coffee
No. A ‘few’ and not ‘all’ German locals on the beach liked coffee (because all locals who like tea also like coffee). We are told that all locals who like tea also like coffee, but this does not mean that all locals like tea to begin with, and not all locals are German, as we only know those on the beach were German.
- Some Germans like tea
Yes. Some Germans are locals as we are told the locals on the beach were German, and some locals must like tea, so some Germans therefore must like tea.
- Some Germans do not like eggs
Yes. All the locals on the beach were German, and none of them liked eggs, therefore it is possible that some Germans do not like eggs.
- The locals on the beach who liked tea also liked photography
Yes. We know that some locals like tea, so it is possible that there are some locals on the beach who like tea. All locals on the beach liked photography, therefore the conclusion does follow.
- All locals on the beach who liked photography, also liked coffee
No. We don’t know for sure that there were locals on the beach who liked coffee, as we don’t know whether there were locals on the beach that liked tea. We know some locals like tea but cannot say that all locals like tea, even though we know all locals on the beach liked photography. Therefore, the conclusion does not follow.
Shorthand method:
All L = T à C
All L on beach = G
No L on beach = E
All L on beach = P
Some L = T
In this shopping centre, not all shops sell clothes. However, all shops in the shopping centre are at least 300 square metres, except for 2 which only sell books.
Explanation
- Some clothes shops are exactly 300 square metres
No. We know that not all shops sell clothes, which means that some shops will sell clothes. However, we do not know whether these shops are 300 metres, as they may be more.
- Tesco is a shop that sells food. It less than 300 square metres.
No. We do not know if this shop is in the shopping centre, therefore we cannot tell if it is 300 square metres.
- Not all clothes outlets in this shopping centre that are 300 square metres are shops.
No. We are not given any information on any clothes outlets other than clothes shops, so we cannot draw this conclusion from the passage.
- All shops that sell books are bigger than 300 square metres.
No. The last sentence says that the 2 shops that are not 300 square metres sell books, but we are don’t know whether they are greater or less than 300 square metres.
- All shopping centres have clothes shops and shops which sell books
No. We are only given information on this shopping centre, so cannot draw a general conclusion about all shopping centres.
Keshavi Perera Medicmind Tutor Tue, 12 Jan 2021 00:47:29
Shouldn't the first statement be Yes because if only book stores are less than 300 square meters and there are some clothes shops then it stands that some clothes shops will be 300 square meters?
A scientist is only considered ‘famous’ if they write three or more research papers. Some scientists are celebrities. All celebrities are famous. Some famous people write books.
Explanation
- Only famous people write books
No. We know that some famous people write books but some people who write books may not be famous. Since we are not given any further information on this we cannot draw this conclusion from the passage.
- It is possible that a book has been written by a scientist
Yes. We know that some scientists are famous, and that some famous people write books. Therefore, this is possible.
- All famous people are celebrities
No. Even though we are told that all celebrities are famous, this does not necessarily mean that the reverse is true.
- Some celebrities could be painters
No. We are not given any information on the relationship between celebrities and painters so we cannot draw this conclusion.
- Rachel, a scientist, wrote 2 research papers, so she must be a celebrity.
No. We know Rachel is not considered famous as she wrote less than 3 research papers, so therefore cannot be a celebrity.
Some bears are mammals. No mammals are birds. All birds have wings.
Explanation
- Some bears are birds
No. We know some bears are mammals and that no mammals are birds. We are not given any information on the relationship between bears and birds, so cannot draw this conclusion.
- No birds are mammals
Yes. We know that no mammals are birds, so the reverse must also be true.
- Some bears are not birds
Yes. The bears that are mammals cannot be birds.
- No mammals have wings
No. We don’t know the relationship between mammals and wings but there is a possibility that a mammal could have wings, so the conclusion does not follow.
- Some birds have wings
Yes. All birds have wings therefore some birds will also have wings.
All boots are snoops and some boots are drones. Most drones are welps.
Explanation
- Most welps are drones
No. It is true that most drones are welps but we cannot say that the reverse is true.
- Some snoops are drones
Yes. The snoops which are boots are also drones. This is because all boots are snoops and some of these boots which are snoops are also drones.
- Some boots are welps
No. We cannot determine if there is a relationship between boots and welps, so we cannot draw this conclusion.
- All snoops are boots
No. The reverse is true but we don’t have enough information to support this conclusion.
- No snoops are welps
No. We don’t know the relationship between snoops and welps so cannot make this conclusion.
Salmon and Tuna are both types of fish. All fishes are sharks. Only angry sharks eat humans. Sharks are always pink.
Explanation
- If a shark eats a human, it must be angry
Yes. We are told that sharks only eat humans if they are angry, so the conclusion does follow.
- All salmons are sharks
Yes. We know that the salmon is a type of fish, and all fishes are sharks, so a salmon must be a shark.
- Some tuna fish are pink
Yes. We know that tuna is a type of fish, and that all fishes are sharks, and all sharks are pink, so tuna fish must therefore be pink.
- A tuna cannot be a shark
No. Like above, we are told that all fishes are sharks, so a tuna fish must be a shark.
- No salmons eat humans
No. A salmon is a type of fish and is therefore a shark. If a shark is angry, they can eat humans, so a salmon could eat a human if they are angry.
Not all people present at the conference were research associates, but all the research associates present at the conference were over 60 and some research associates were not male.
Explanation
- Some males at the conference were over 60.
Yes. All the research associates were over 60 and if some research associates were not male that means some were, so there would be some males over 60.
- Some over 60s at the conference were both research associates and male
No. It is true that some over 60s would have been research associates as we are told this in the passage. We also know that there were some male research associates, but this does not necessarily mean that we can have a male research associate over the age of 60, as the male research associates could be younger.
- All the over 60s at the conference were either research associates or male.
No. We are not given any information on what other types of people there were – we only know that research associates were present and others, so we cannot draw this conclusion.
- Not all over 60s at the conference who were research associates were male.
Yes. We know that the research associates were over 60 and that there are only some male research associates, so we can assume there are also some female research associates over the age of 60.
- All the females at the conference who were over 60 were also research associates.
No. We are not told if there were any other professionals who were also over 60 so we cannot draw this conclusion.
Poppy Medicmind Tutor Sun, 30 Aug 2020 11:54:53
For the second statement, if we know that some research associates were male and that ALL research associates were over 60 then surely that means that some over 60s at the conference were both research associates and male (making the statement YES and not no) ?
Brian is a librarian. None of the books are kept in the storeroom apart from books by JK Rowling or Anthony Horowitz. All books are enjoyable reads except for dystopian novels.
Explanation
- Either a book is a dystopian novel, or it is an enjoyable read
Yes. We are told that all books are enjoyable except dystopian novels, so if it is not a dystopian novel it must be enjoyable.
- If a book is in the storeroom it is one by JK Rowling
No. Books in the storeroom will either be by JK Rowling or Anthony Horowitz, so it could be Anthony Horowitz, therefore the conclusion does not follow.
- If the library is an enjoyable read it cannot be JK Rowling
No. We are not told whether books by JK Rowling are dystopian or not, so they will be enjoyable if they are not dystopian and won’t be enjoyable if they are dystopian.
- If someone takes a book from the storeroom they will not enjoy it
No. Books in the storeroom could still be enjoyable as long as they are not dystopian novels.
Some leaves are green. Bushes are green. Forests are made up of leaves and bushes. Bush A can be found in this forest.
Explanation
- Rose bushes can be found in this forest
No. We are not given any information on other types of bushes in the forest so we cannot draw this conclusion.
- Some leaves are yellow
No. Although this might be true, we don’t have enough information to prove this, so the conclusion does not follow.
- This forest is completely green
No. Although this could be true if the leaves were also green, we don’t know whether they are, we only know that a bush which is green can be found, so we cannot draw this conclusion.
- Bushes have leaves
No. Bushes are green, but we are not told explicitly that bushes have green leaves, so we cannot assume this.
- Some bushes are found in forests
Yes. We know that bush A can be found in this forest, therefore we know that some bushes are found in forests.
Most lions can roar, but no individual that roars can fly.
Explanation
- Most lions cannot fly
Yes. Most lions roar and things that roar cannot fly, so most lions cannot fly.
- If something can fly, they cannot roar
Yes. We know that nothing that roars can fly, so the reverse must also be true.
- Some things that roar do not fly
Yes. As above
- No lions can fly
No. We know that most lions can roar, but this also implies that some do not roar. Those that do not roar might be able to fly so we cannot rule out this possibility.
- Most things that roar are lions
No. We are not given any information on other individuals that can roar. There may be more of other individuals that roar than lions, so this does not follow.
Kiwis and bananas are both types of fruit. Neither of them have seeds but they both have peel. Zucchinis have peel but are not a fruit.
Explanation
- Zucchinis have seeds
No. We are not told this information in the passage so we cannot draw this conclusion.
- All three of bananas, kiwi and zucchinis have peel
Yes. We are told explicitly that all 3 of these have peel.
- If a fruit has a peel, it must be a banana or kiwi
No. We are not given any information on whether any other fruit may have peel as we are only told about bananas and kiwis, so we cannot draw this conclusion with insufficient information.
- If a fruit has no seeds, it cannot be a kiwi
No. Kiwis do not have seeds so a fruit with no seeds can be a kiwi.
- Either bananas or kiwis have seeds
No. We are not given enough information in the passage to make this conclusion.
All juices are non-alcoholic drinks and all non-alcoholic drinks are beverages. Juices are not beers.
Explanation
- Beers are alcoholic drinks
No. We are not given this information in the passage so cannot draw this conclusion.
- Beers are beverages
No. We are not given this information in the passage so cannot make this conclusion.
- Some non-alcoholic drinks are not beers
Yes. We know that juices are not beers and that they are non-alcoholic drinks, so we know that some non-alcoholic drinks are not beers.
- All non-alcoholic drinks are juices
No. All juices are non-alcoholic drinks but this does not mean that the reverse is true.
- If a non-alcoholic drink is a juice, it is a beverage
Yes. All non-alcoholic drinks are beverages and all juices are non-alcoholic drinks, so all juices must be beverages.
All mammals have fur and are warm blooded. Some mammals are elephants with large ears. Some elephants have larger ears than others.
Explanation
- All elephants are warm blooded
No. We don’t know whether all elephants are mammals or whether just the ones with large ears are mammals.
- Some elephants have fur and are warm blooded
Yes. We are told that some elephants are mammals so therefore they must have fur and be warm blooded.
- All elephants with large ears are mammals
No. We know that some mammals are elephants with large ears but this does not mean that the reverse is true.
- There are some elephants with small ears
No. We know that some elephants have larger ears than others, but those with smaller ears may not necessarily have what is considered ‘small’ ears.
- Not all mammals have fur, are warm blooded, and have large ears
Yes. We know that some elephants have all these features, but there may also be some mammals that are not elephants and do not have large ears but that will have fur and are warm blooded.
All of Susan’s shirts are blue. All of Jack’s shirts are orange. This shirt is either Susan’s or Jack’s.
Explanation
- This shirt is either orange or Susan’s
Yes. Susan’s shirts are all blue and Jack’s shirts are all orange so if this shirt is orange it will be Jack’s and if it is Susan’s it will be blue.
- All shirts are either blue or orange
No. We only know about this shirt, we do not know about other shirts so cannot draw this conclusion.
- This shirt is either orange or Jack’s
No. If the shirt is not orange it must be Susan’s so the conclusion does not follow.
- If this shirt is orange, it cannot be Susan’s
Yes. If the shirt is orange it must be Jack’s.
- If a shirt is blue, it must be Susan’s
No. We only know that if THIS shirt is blue it will be Susan’s but cannot generalise for all shirts.
Not all people present at the book fair were students, but most students were under the age of 16 and some students were not boys.
Explanation
- Some boys at the book fair were under the age of 16
Yes. We know that some students were boys and that all students were under the age of 16, so this conclusion is correct.
- Some people under the age of 16 at the book fair were male students
Yes. Students at the book fair were under the age of 16 and some were male so there could be male students present at the fair under the age of 16.
- Everyone under the age of 16 at the book fair were either students or boys
No. There could be male students under 16 at the fair.
- Not everyone under the age of 16 who were students were boys
Yes. We know that not all the students were boys and that all the students were under 16, so some male students present must also be boys under 16.
- All the boys at the book fair who were under the age of 16 were also students
No. We are not given any information of those who aren’t students at the book fair, but we do know that not everyone at the book fair was a student, so there could be people who aren’t students who are under the age of 16 and are also male.
Everyone in the museum except for Jane, like drinking coffee. More than 1 person likes butter on their toast.
Explanation
- Jane likes butter on her toast
No. We know that more than 1 person likes butter on their toast, but this does not necessarily mean that Jane does.
- If a person in the museum does not like butter on their toast, they must like drinking coffee.
No. The person who does not like butter on their toast might be Jane, who does not like coffee.
- If a person in the museum does not like drinking coffee, it must be Jane
Yes. Everyone except Jane likes coffee so the conclusion follows.
- If only two people in the museum like butter on their toast, one must be Jane
No. We do not know Jane’s opinion on butter on toast so cannot make this conclusion.
- Someone in the museum likes drinking coffee and butter on their toast.
Yes. It is possible for someone to like drinking coffee and also have butter on toast because more than 1 person likes butter on their toast and everyone except jane likes coffee.
Camel milk is always sour and never delicious. All Cow’s milk is delicious and no cow milk is sour. This milk is either cow’s milk or camel milk.
Explanation
- This milk is either delicious or sour
Yes. If the milk is delicious it is Cow’s milk if it is sour it is Camel milk.
- If this milk is not delicious it must not be Cow’s milk.
Yes. Cow’s milk is delicious but camel milk is sour, so it must be Camel’s milk if it is not delicious.
- Milk either comes from camels or cows
No. This is a generalized statement that we cannot make from the information given in the passage.
- This milk is sour or camel milk
No. If the milk is sour it will be Camel milk, if it is not sour it will be cow’s milk.
- No cow’s milk is disgusting
Yes. We are told that all cow’s milk is delicious so it cannot be disgusting.
All diamonds are shiny and some metals are shiny. All shiny things can become dull over time.
Explanation
- If something is dull, it must have once been a shiny metal
No. Some metals are shiny, but some may not be shiny, so it could have been dull from the start.
- A dull metal used to be shiny
No. Like above, some metals can also be dull from the start.
- Graphite is a metal. It is dull.
No. We are not given any information about graphite so cannot assume it is not shiny.
- All shiny things are metals
No. We are only told about metals being shiny but there could be some shiny things that are not metals.
- All diamonds become dull over time
No. All diamonds are shiny and all shiny things CAN become dull over time, but not all of them will, so the conclusion does not follow.
At costa I can either buy an iced coffee or a hot chocolate. Iced coffee is expensive.
Explanation
- Hot chocolate is cheaper than iced coffee
No. We know that iced coffee is expensive but we don’t know the cost of hot chocolate relative to iced coffee, so cannot make this conclusion.
- Costa only sells iced coffee or hot chocolate
No. We know I can either buy an iced coffee or hot chocolate but that does not mean they don’t sell other drinks.
- All hot chocolate is not expensive
No. Again, we aren’t given any information on the price of hot chocolate so cannot make this conclusion.
- Some costa drinks are expensive
Yes. Iced coffee is expensive and is sold at costa, so some costa drinks must be expensive.
- At costa the drinks are either made from coffee or cocoa
No. We do not know that hot chocolate is made from cocoa as we are not told this in the passage, so we cannot make this conclusion.
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