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# Let X = {a, b, c, d}. What is {A: A ∈ P(X) and |A| = 2}?

A set is a collection of elements. A powerset is a collection of all the possible sets that can be formed of the given set.

## Answer: {A: A ∈ P(X) and |A| = 2} = {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}}

Let's find the set {A: A ∈ P(X) and |A| = 2}

**Explanation:**

Given that X = {a, b, c, d}

P (X) = { Ø, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {b, c, d}, {a, c, d}, {a, b, c, d}}

A is a subset of P(X) that contains only two elements as |A| = 2

A = {a, b} or {a, c} or {a, d} or {b, c} or {b, d} or {c, d}

### Thus, {A: A ∈ P(X) and |A| = 2} = {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}}

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