Question

U = {a, f, g, l, n, r, u} X = {a, g, n, u} Y = {a, f, g} Z = {f, g, l, n, r} Find the following set: (Z ∪ X') ∩ Y

a. {g}
b. {f, l, r}
c. {a, g}
d. {n}

Answer 1

To find the set (Z ∪ X') ∩ Y, first find the complement of X, then find the union of Z and X', and finally find the intersection with Y. The answer is {f, g}.

Step-by-step explanation:

To find the set (Z ∪ X') ∩ Y, we need to break it down step by step:

1. First, find the complement of X, denoted as X'. This means finding all the elements in the universal set U that are not in X. In this case, X' = {f, l, r, n}.
2. Next, find the union of Z and X'. The union of two sets is all the elements that are in either set. In this case, Z ∪ X' = {f, g, l, n, r}.
3. Finally, find the intersection of the above result with Y. The intersection of two sets is all the elements that are common to both sets. In this case, (Z ∪ X') ∩ Y = {f, g}.

The answer is

{f, g}