Answer to Question #323120 in Discrete Mathematics for Jetro

Question

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 A is not a subset of B, because the prime number 2 belongs to A, but does not belong to B, as 2 is not odd. B also is not a subset of A, because the odd number 9 belongs to B, but is not a prime number, and therefore it does not belong to A.

2 The fact that A is not a subset of B is sufficient to assert that A and B are not equal.