Hey, what if they mention proper subset instead of subset, then will it be 2^n ?

1 vote

A is a non-empty set having n elements. P and Q are two subsets of A, such that P is a subset of Q. Find the number of ways of choosing the subsets P and Q.

- 4
^{n} - 3
^{n} - 2
^{n} - n
^{2}

2 votes

Best answer

1 vote

Lets take example let A={1,2}

Q can be 0 element set, then no of 0 element sets =1 .. Then its subsets possible ie P

=2^0 =1

Q can be 1 element set, no of such sets s =2 .. no of subsets in each = 2^1

Q can be 2 element sets =1..

no of subsets possible =2^2

Total combinations=1+4+4=9

Since correct option must be true for all cases including 2 element set , correct ans is 3 ^n

Q can be 0 element set, then no of 0 element sets =1 .. Then its subsets possible ie P

=2^0 =1

Q can be 1 element set, no of such sets s =2 .. no of subsets in each = 2^1

Q can be 2 element sets =1..

no of subsets possible =2^2

Total combinations=1+4+4=9

Since correct option must be true for all cases including 2 element set , correct ans is 3 ^n