Questions: Sketch a Venn diagram like the one shown to the right, and use shading to show the set B ∩ (A′ ∩ C′).

Sketch a Venn diagram like the one shown to the right, and use shading to show the set B ∩ (A′ ∩ C′).
Transcript text: Sketch a Venn diagram like the one shown to the right, and use shading to show the set $B \cap\left(A^{\prime} \cap C^{\prime}\right)$.
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Solution

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Solution Steps

Step 1: Find A'

A' is the complement of A, meaning everything outside of A.

Step 2: Find C'

C' is the complement of C, meaning everything outside of C.

Step 3: Find the intersection of A' and C' (A' ∩ C')

This represents the area that is both outside of A and outside of C.

Step 4: Find the intersection of B and (A' ∩ C') (B ∩ (A' ∩ C'))

This represents the area that is in B and also outside of both A and C. This corresponds to the area shaded in option A.

Final Answer

\\(\boxed{A}\\)

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