Answer to Question #306261 in Linear Algebra for Wes

Question

2.8. Let P be the property “is a prime number” and O be the property “is an odd

integer.” Consider the sets A = {x ∈ N : P(x)} and B = {x ∈ N : O(x)}.

1. Examine A and B with respect to the subset relation. What can you conclude? Justify your

answer.

2. Are A and B equal? Justify your answer.

Answer 1

1.

All prime numbers are odd numbers but not all odd numbers are prime numbers. Therefore A is a subset of B

2.

A and B are not equal but A is in B