Module 2: If set S entails A

Question 1

S: {“If the sun rises tomorrow, then Vancouver is a small city,” “If Vancouver is a small city, then China is a big country,” “If China is a big country, then Jill works at SFU”}
A: If the sun rises tomorrow, then Jill works at SFU

Answer 1

S entails A

Question 2

S: {“Some lawyers are rich people,” “Some rich people are women”}
A: Some lawyers are women

Answer 2

S does NOT entail A.

• Truth of “some lawyers are rich people” and “Some rich people are women” does NOT guarantee the truth of “Some lawyers are women”
• Imagine a world where all lawyers are male and some of these male lawyers are rich. In that same world there also happens to be a number of rich women doctors. This is a case where “Some lawyers are rich people” would be true. “Some rich people are women” would be true too, but “some lawyers are women” would be false. Since it IS possible for the members of S to be true and A false
• so S does not entail A

Question 3

S: {“Bertrand Russell has red hair,” “All mathematicians have red hair”}
A: Bertrand Russel is a mathematician

Answer 3

S does NOT entail A
- just because Bertrand Russell shares the same property of having red hair with all mathematicians does not mean that he is a mathematicians himself.

Question 4

S: {“If it rains tomorrow, we will not go on the picnic,” “We will go on the picnic”}
A: It will not rain tomorrow

Answer 4

S entails A

Question 5

S: {“Either Tom likes tennis or Tom likes mountain biking,” “If Tom likes tennis, then he owns a tennis racket,” “If Tom likes mountain biking, then he owns a mountain bike,” “Tom does not own a tennis racket”}
A: Tom owns a mountain bike

Answer 5

S entails A