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If A = {a, b, c, d, e}, B = {a, c, e, g} and C = {b, e, f, g}. Find (A ∪ B) ∩ (A ∪ C) ?

If A = {a, b, c, d, e}, B = {a, c, e, g} and C = {b, e, f, g}. Find (A ∪ B) ∩ (A ∪ C) ? Correct Answer {a, b, c, d, e, g}

Concept:

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Calculation:

Given: A = {a, b, c, d, e}, B = {a, c, e, g} and C = {b, e, f, g}

As we know that, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Here, we have to find the value of (A ∪ B) ∩ (A ∪ C)

i.e we have to find the value of A ∪ (B ∩ C)

⇒ B ∩ C = {e, g}

⇒ A ∪ (B ∩ C) = {a, b, c, d, e} ∪  {e, g} = {a, b, c, d, e, g}

Hence, (A ∪ B) ∩ (A ∪ C) = {a, b, c, d, e, g}

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