Question

refer to the venn diagram below, and indicate which region(s) should be shaded to represent the set ((a cap b)cup c). separate multiple answers with a comma, if necessary.
the set of region(s) in the venn diagram that will be shaded is (square).

Explanation:

Step1: Identify \(A \cap B\)

Region \(II\) (only overlap of \(A\) and \(B\))

Step2: Find \((A \cap B)'\)

All regions except \(II\): \(I, III, IV, V, VI, VII, VIII\)

Step3: Union with \(C\)

Add regions of \(C\) (\(IV, V, VI, VII\)) to \((A \cap B)'\); combine unique regions: \(I, III, IV, V, VI, VII, VIII\)

Answer:

I, III, IV, V, VI, VII, VIII