Question

Sets A, B, and C are subsets of the universal set U.These sets are defined as follows.U={f, g, h, p, q, r, x, y, z)A={f, g, h, q, r}B={q, r, x, z)C={h, p,q,z}Find (C ⋂ B) U A'Write your answer in roster form or as Ø.(C ⋂ B) U A' =

Answer 1

To find (C ⋂ B) ⋃ A', the steps are:

1. Find the intersection or the common elements of Set C and Set B.

Based on the list of elements of Set C and B, the common elements of both sets are q and z. Hence, (C ⋂ B) = {q, z}.

2. Next, find the complement of A. Complement of A contains the elements that are in the universal set but not in A.

Since A contains {f, g, h, q, r} then, A' must have {p, x, y, z}. Therefore, A' = {p, x, y, z}.

3. Next, the symbol ⋃ means to combine. Therefore, we need to combine or join the elements of (C ⋂ B) and A'.

The elements of A' are p, x, y, and z while the elements of (C ⋂ B) are q and z.

Therefore, joining the elements, (C ⋂ B) ⋃ A' = {p, q, x, y, z}.

Note that we will only list the elements once. Even though "z" occurred on both sets, we will only list it once.

ANSWER:

(C ⋂ B) ⋃ A' = {p, q, x, y, z}