Multiple Choice

1. Determine whether the conclusion reached in the following set of logic statements is valid or invalid. All cats are mammals. All mammals are animals. $\therefore$ All cats are animals.

   Valid

   Invalid

   The conclusion is sometimes true, sometimes false

   Cannot be determined without a specific example

2. Determine whether the conclusion reached in the following set of logic statements is valid or invalid. Some students like art. No teachers like art. $\therefore$ No students are teachers.

   Valid

   The premises are contradictory

   Invalid

   The conclusion is sometimes true

3. Consider the sets: $P = \{ \text{polygons} \}$, $T = \{ \text{triangles} \}$, $C = \{ \text{circles} \}$. Which option correctly describes both "All triangles are polygons" AND "No circles are polygons"?

   All P is contained in T, and No C is contained in P.

   All T is contained in P, and No C is contained in P.

   All T is contained in P, and Some C is contained in P.

   Some T is contained in P, and All C is contained in P.

4. Determine whether the conclusion reached in the following set of logic statements is true, assuming the premises are true. All birds have feathers. All chickens are birds. $\therefore$ All chickens have feathers.

   True, because the conclusion logically follows from the true premises.

   Cannot be determined.

   False, because some chickens cannot fly.

   The premises are not always true.

5. Determine whether the conclusion reached in the following set of logic statements is valid or invalid. All fish live in water. No birds live in water. $\therefore$ No birds are fish.

   Cannot be determined

   Valid

   Invalid

   The premises are contradictory

6. State whether the conclusion reached in the following set of logic statements is valid or invalid. All cats are mammals. All mammals are animals. $\therefore$ All cats are animals.

   Cannot be determined without more information.

   Valid, because if cats are a subset of mammals, and mammals are a subset of animals, then cats must be a subset of animals.

   Invalid, because some cats are not mammals.

   Invalid, because some mammals are not animals.

7. State whether the conclusion reached in the following set of logic statements is valid or invalid. Some students like maths. Some students like science. $\therefore$ Some students like both maths and science.

   Valid, because if some students like maths and some like science, there must be an overlap.

   Invalid, because the groups of students who like maths and those who like science could be completely different, with no overlap.

   Valid, because all students eventually like both subjects.

   Cannot be determined definitively without knowing which specific students like which subject.

8. Consider the following logic statements: All dogs are canines. No cats are canines. Which of the following statements accurately describes the relationship between dogs and cats, based on these premises?

   All cats are dogs.

   No dogs are cats.

   Some dogs are cats.

   All dogs are cats.

9. Determine the valid conclusion from the following set of logic statements: All birds have feathers. My pet is a bird.

   All pets have feathers.

   My pet has feathers.

   Some birds do not have feathers.

   My pet might have feathers, but it's not certain.

10. State whether the conclusion reached in the following set of logic statements is valid or invalid. No fish can fly. All salmon are fish. $\therefore$ No salmon can fly.

    Invalid, because some fish might be able to fly.

    Valid, because if all salmon are fish, and no fish can fly, then it logically follows that no salmon can fly.

    Invalid, because salmon are a type of fish, which doesn't directly mean they can't fly.

    Cannot be determined without knowing more about salmon.

11. State whether the conclusion reached in the following set of logic statements is valid or invalid. All dogs are mammals. All cats are mammals. $\therefore$ All dogs are cats.

    Cannot be determined without knowing more about specific animals.

    Invalid, because while both dogs and cats are mammals, the premises do not establish any direct relationship or overlap between the set of dogs and the set of cats.

    Valid, because both dogs and cats are mammals.

    Valid, because some dogs and some cats share traits.

12. Determine the valid conclusion from the following set of logic statements: All students in Grade 8 wear uniforms. Some students in Grade 8 play sport.

    All students who wear uniforms play sport.

    No students who play sport wear uniforms.

    All students who play sport wear uniforms.

    Some students who wear uniforms play sport.

13. State whether the conclusion reached in the following set of logic statements is valid or invalid. Some birds are yellow. Some yellow things are flowers. $\therefore$ Some birds are flowers.

    Cannot be determined, as we don't know which specific yellow things are birds or flowers.

    Invalid, because the yellow birds and the yellow flowers could be entirely distinct groups, with no bird also being a flower.

    Valid, because if both birds and flowers can be yellow, there must be a connection.

    Valid, because some birds might land on yellow flowers.

14. Given the sets: A = {animals}, B = {birds}, F = {flying creatures}. Which of the following premise statements correctly describes the relationship where all birds are animals, and some birds are flying creatures?

    Some A is contained in F, and no B is contained in A.

    All F is contained in B, and all A is contained in B.

    All B is contained in F, and some A is contained in B.

    All B is contained in A, and some B is contained in F.

15. State whether the conclusion reached in the following set of logic statements is valid or invalid. All musicians are artists. John is a musician. $\therefore$ John is an artist.

    Invalid, because not all artists are musicians.

    Invalid, because John might be a musician but not a performing artist.

    Valid, because if the set of musicians is entirely contained within the set of artists, and John is in the set of musicians, then John must also be in the set of artists.

    Cannot be determined without knowing John's specific artistic skills.

16. State whether the conclusion reached in the following set of logic statements is valid or invalid. Some fruit is red. An apple is a fruit. $\therefore$ An apple is red.

    Valid, because an apple is a type of fruit, and some fruit is red.

    Valid, because apples are often red.

    Invalid, because while some fruit is red and an apple is a fruit, the premises do not guarantee that *this specific apple* or *all apples* are red.

    Cannot be determined without seeing the specific apple.

17. Determine the valid conclusion from the following set of logic statements: No fish live on land. All salmon are fish.

    No salmon live on land.

    All salmon live on land.

    Not all fish are salmon.

    Some salmon might live on land.

18. State whether the conclusion reached in the following set of logic statements is valid or invalid. All brain surgeons are clever. Some Australians are brain surgeons. $\therefore$ Some Australians are clever.

    Invalid, because some Australians might not be clever.

    Valid, because if some Australians are in the group of brain surgeons, and all brain surgeons are in the group of clever people, then those specific Australians must also be clever.

    Cannot be determined without more information about Australian cleverness.

    Invalid, because not all clever people are brain surgeons.

19. State whether the conclusion reached in the following set of logic statements is valid or invalid. Some footballers are overweight. No athlete is overweight. $\therefore$ No athletes are footballers.

    Valid, because if no athletes are overweight, they cannot be among the overweight footballers.

    Cannot be determined without knowing specific examples of athletes and footballers.

    Valid, because athletes are typically fit and not overweight, so they can't be footballers.

    Invalid, because there could be footballers who are *not* overweight, and these footballers could also be athletes, meaning the sets of athletes and footballers are not necessarily disjoint.

20. Determine the valid conclusion from the following set of logic statements: All students are learners. All learners are thinkers.

    All thinkers are students.

    Some learners are not students.

    No students are thinkers.

    All students are thinkers.