Let X = {A, B, C, D}. What Is { A: A ∈ P(X) And |A| = 2 }?

Solution: 

Given a set X = {A, B, C, D}

We know P(X) represents the power set of A and the number of elements in P(X) is 2ⁿ, where n represents the number of elements in the set X.

Here P(X) = 2⁴ = 16.

The elements of P(X) = {Ø, (A, B, C, D), (A), (B),(C), (D), (AB), (BC), (CD), (DA), (AC), (BD), (ABC), (BCD), (CDA), (ABD)}

By |A| = 2 means the number of elements present in a subset of X having two elements in it.

Therefore, { A: A ∈ P(X) And |A| = 2 } = {(AB), (BC), (CD), (DA), (AC), (BD)}

Let X = {A, B, C, D}. What Is { A: A ∈ P(X) And |A| = 2 }?

Summary:

Given X = {A, B, C, D}, { A: A ∈ P(X) And |A| = 2} = {(AB), (BC), (CD), (DA), (AC), (BD)}