If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0 $\geq$ x $\geq$ 6}, find x $\cap$ (Y' $\cup$ Z)

Analyze the question: We need X ∩ (Y' ∪ Z), where the universal set U is described as {x : 0 ≥ x ≥ 6}. This is almost certainly a typing error for 0 ≤ x ≤ 6, so U = {0, 1, 2, 3, 4, 5, 6} (integers).

Concept:

• Y' (complement of Y) means the elements of U that are not in Y.
• ∪ combines the elements of both sets.
• ∩ picks only the elements common to both sets.

Solution:

1. Y = {1, 2, 3, 4}, so Y' = U − Y = {0, 5, 6}.

2. Y' ∪ Z = {0, 5, 6} ∪ {1, 3} = {0, 1, 3, 5, 6}.

3. X ∩ (Y' ∪ Z) = {0, 2, 4, 6} ∩ {0, 1, 3, 5, 6} = {0, 6}.

Answer: {0, 6}, which is option C.

Note on the question: The universal set as written (0 ≥ x ≥ 6) is impossible, since no number is both at most 0 and at least 6. The intended meaning is 0 ≤ x ≤ 6, and that gives option C.

Tip: In set problems with complements, always write out the universal set first, then find the complement, then work through the brackets before the final intersection. Do it in the order: complement → union → intersection.