Questions: For the universal set, U=g, h, p, q, r, x, y, complete the parts below. Write your answers in roster form or as ∅. (a) Suppose we know that A′=g, p, r, x. Then what would A have to be? A= (b) Suppose C=h, p, q, y. Then what is C′ ? C′=

(a) Suppose we know that \( A^{\prime}=\{g, p, r, x\} \). Then what would \( A \) have to be?

Identify the universal set and the complement of \( A \).

The universal set is \( U = \{g, h, p, q, r, x, y\} \), and \( A^{\prime} = \{g, p, r, x\} \).

Find \( A \) by taking the complement of \( A^{\prime} \).

\( A = U - A^{\prime} = \{h, q, y\} \).

\[ \boxed{A = \{h, q, y\}} \]

(b) Suppose \( C=\{h, p, q, y\} \). Then what is \( C^{\prime} \)?

Identify the universal set and the set \( C \).

The universal set is \( U = \{g, h, p, q, r, x, y\} \), and \( C = \{h, p, q, y\} \).

Find \( C^{\prime} \) by taking the complement of \( C \).

\( C^{\prime} = U - C = \{g, r, x\} \).

\[ \boxed{C^{\prime} = \{g, r, x\}} \]

\[ \boxed{A = \{h, q, y\}}
\boxed{C^{\prime} = \{g, r, x\}} \]