# 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 elements that can be formed of the given set.

## Answer: P(x) is a powerset of set x. Every element of set x contains 2.

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, b, c, d) }

a = { (a), (a, b), (a, c), (a, d), (a, b, c), (a, b, d), (a, c, d) }

| a | = 2

Let A = {1, 2, 3}

P (a) = { ( Ø ), (1), (2), (3), (1, 2), (1, 3), (2, 3), (1, 2, 3) }

x = { (2), (1, 2), (2, 3), (1, 2, 3) }