Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Question

Philoid · Accepted Answer

Given: A = {1, 2} and B = {3, 4}

(A × B) = {(1,3), (1,4), (2,3), (2,4)}

Number of elements in (A × B) = 4

⇒ n(A × B) = 4

Then number of subsets of set (A × B) = 2ⁿ = 2⁴ = 16

⇒ number of subsets of set (A × B) = 16

These are:

{ϕ}, {(1,3)}, {(1,4)}, {(2,3)}, {(2,4)}, {(1,3),(1,4)}, {(1,3),(2,3)}, {(1,3),(2,4)}, {(1,4),(2,3)}, {(1,4),(2,4)}, {(2,3),(2,4)}, {(1,3),(1,4),(2,3)}, {(1,3),(1,4),(2,4)}, {(1,4),(2,3),(2,4)}, {(1,3),(2,3), (2,4)}, {(1,3),(1,4),(2,3),(2,4)}.