Question

Let S be the set of integers that are multiples of 6, and let T be the set of integers that are multiples of 2.

(a) Is S ⊆ T? If so, prove the statement. Otherwise, explain why the statement is false by providing a counterexample.
(b) Is T ⊆ S? If so, prove the statement. Otherwise, explain why the statement is false byproviding a counterexample.

Answer 1

S is a subset of T and T is a subset of S.

Step-by-step explanation:

a. To determine if S is a subset of T, we need to check if every element in S is also in T. S is the set of integers that are multiples of 6, so S = {6, 12, 18, ...}. T is the set of integers that are multiples of 2, so T = {2, 4, 6, 8, ...}. Since every element in S is also in T, we can conclude that S ⊆ T.

b. To determine if T is a subset of S, we need to check if every element in T is also in S. S is the set of integers that are multiples of 6, so S = {6, 12, 18, ...}. T is the set of integers that are multiples of 2, so T = {2, 4, 6, 8, ...}. Since every element in T is also in S, we can conclude that T ⊆ S.