Question

Let U={a,b,c,d,e,f,g,h). Let X, Y, and Z be subsets of U such that X = {a,c,d,f,g} Y = {b,c,e,g,h} Z={c,d,g} Find (X-Y)UZ

Answer 1

The set (X - Y)
`\cup Z\)` is {a, d, g}.

Step-by-step explanation:

To find
`\((X - Y) \cup Z\)`, we first need to determine X - Y, which represents the elements that are in X but not in Y. From the given sets, X = a, c, d, f, g} and Y = {b, c, e, g, h} Therefore, X - Y = {a, d, f}. Next, we take the union of this set with Z = {c, d, g}. The union of these sets,
`\((X - Y) \cup Z\)`, is {a, d, g}.

In summary,
`\((X - Y) \cup Z\)`comprises the elements that are in X but not in Y, along with the elements in Z. The resulting set is {a, d, g}.

Understanding set operations, such as subtraction and union, is essential in set theory. Subtracting one set from another gives the elements that are exclusive to the first set, and the union combines elements from multiple sets, eliminating duplicates.

The final answer, {a, d, g}, represents the set (X - Y)
`\cup Z\)`, satisfying the specified conditions based on the given sets X, Y, and Z within the universal set U.