Question

Which statements about x are true? Check all that apply.

1.x is not in a
2.x is in b
3.x is not in c
4.x is in a union b
5.x is in a intersection b

Answer 1

To determine which statements about element x are true, information about its membership in sets a, b, and c is necessary. The truth of statements about union and intersection depends on x being in one or both sets respectively.

Step-by-step explanation:

When analyzing the statements about x, it's important to understand the concepts of set membership and set operations such as union and intersection. Here is an analysis of each statement:

1. x is not in a - This statement cannot be evaluated as true or false without specific information about set a and element x.
2. x is in b - Similar to the first statement, whether this is true depends on the contents of set b and whether x is a member.
3. x is not in c - The truth of this statement also cannot be determined without information about set c and element x.
4. x is in a union b - If either of the previous statements 1 or 2 is true, this would also be true, as union implies that x is in at least one of the sets a or b.
5. x is in a intersection b - For this statement to be true, x must be a member of both sets a and b. This is only true if the second statement is true and x is also in set a.

Without details about the sets, we cannot definitively state which of these statements about x are true. Each one depends on the specific content of the sets involved.