Question

Find the number of proper subsets of the set formed by union of the two given sets.
A = {1, 2, 3} B = {a, 1, b, 2, 3, c}

• A. 32
• B. 31
• C. 63
• D. 64

Answer 1

The correct option is C 63

Given that:
set A = {1, 2, 3}
set B = {a, 1, b, 2, 3, c}
A U B = {a, 1, b, 2, 3, c}
Then, n(A U B) = 6.
We know that the number of proper subsets of a set with n elements $=2^n-1$

Number of proper subsets of the set $A\cup B=2^6-1=64-1=63$