Syllogisms Part 2

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

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.

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.

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

No. Some birds have wings therefore some birds will not have wings.

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.

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.

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

Yes. 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.