Since x is an integer, we have
K = {…, -6, -5, -4, -3, -2}
Y = {2, 3, 4, 5}
Z = {…, -1, 0, 1, 2, 3}
Then
(i)
Y U Z = {…, -1, 0, 1, 2, 3, 4, 5}
==> K ∩ (Y U Z) = {…, -6, -5, -4, -3, -2} = K
(ii)
K ∩ Y = { } (empty set)
K ∩ Z = {…, -6, -5, -4, -3, -2} = K
==> (K ∩ Y) U (K ∩ Z) = { } U K = K
(iii) This is a demonstration of the distributive property. That is, the intersection distributes over a union:
K ∩ (Y U Z) = (K ∩ Y) U (K ∩ Z)
