Question

Consider the statements:

a. C⊆A∪B
b. C∖A⊆B
c. CΔ(A∩B)⊆A∪B

Are these statements equivalent?

a. True
b. False

Answer 1

The statements are not equivalent. The answer is False.

Step-by-step explanation:

The statements are not equivalent. Let's break down each statement:

a. C⊆A∪B:

This statement is true if every element in set C is also in either set A or set B, or both.

b. C∆A⊆B:

This statement is true if every element in set C that is not in set A is also in set B.

c. CΔ(A∩B)⊆A∪B:

This statement is true if every element in the symmetric difference of sets C and (A∩B) is also in set A or set B, or both.

To determine if the statements are equivalent, we need to show that if a. is true, then b. and c. must also be true, and if b. is true, then a. and c. must also be true.