Question

Sets A through H are defined as follows.

A = {1, 2, 3, 4}
B = {-1, -2, -3}
C = {-1, 0, 1, 2, 3}
D = {2, 3, 4, 5, 6, 7}
E = {x ∈ Z: x is odd}
F = {x ∈ Z+: x ≤ 7}
G = {x ∈ Z+: x < 7}
H = {x ∈ Z+: x ≤ 6} Indicate whether each statement is true or false.
(a) |A ∩ B| = 1
(b) {1, 2} ⊂ P(A)
(c) G ⊆ H
(d) |C - F| = 1

Answer 1

The evaluation of the statements about sets A-H revealed that only two of the statements were true, and the other two were false based on set theory.

Step-by-step explanation:

To evaluate the given statements about the sets A through H, let's examine each one step by step.

1. |A ∩ B| = 1: To find the intersection of sets A and B, we need to look for common elements. The set A = {1, 2, 3, 4} and the set B = {-1, -2, -3} have no common elements. Therefore, the statement is false.
2. {1, 2} ⊆ P(A): P(A) represents the power set of A, which includes all subsets of A, including {1, 2}. Therefore, the statement is true.
3. G ⊆ H: G is defined as {x ∈ Z+: x < 7} and H as {x ∈ Z+: x ≤ 6}, which means every element of G is indeed in H. Therefore, the statement is true.
4. |C - F| = 1: C minus F (C-F) means we remove the elements of F from C. F contains all positive integers less than or equal to 7. C contains {-1, 0, 1, 2, 3}. The element of C not in F is {-1, 0}. Therefore, the statement is false because |{-1, 0}| = 2.