Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are

Let A and B be such sets, i.e, n (A) = m and n (B) = n So, number of subsets of $A = 2^m$ Number of subsets of $B = 2^n$ According to the question, $2^m - 2^n = 56$ $\Rightarrow \, 2^n (2^{m - n} - 1) = 56 = 2^3.7$ Thus, $n = 3$ and $2^{m - n} - 1 = 7$ $\Rightarrow \, n = 3$ and $m - n = 3 $ Hence, we get n = 3 and m = 6

Two finite sets have $m$ and $n$ elements. The tot

Notes on Operations on Sets

Concepts Used:

Operations on Sets

Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:

1. Union of Sets:

The union of sets lists the elements in set A and set B or the elements in both set A and set B.
For example, {3,4} ∪ {1, 4} = {1, 3, 4}
It is denoted as “A U B”

2. Intersection of Sets:

Intersection of sets lists the common elements in set A and B.
For example, {3,4} ∪ {1, 4} = {4}
It is denoted as “A ∩ B”

3.Set Difference:

Set difference is the list of elements in set A which is not present in set B
For example, {3,4} - {1, 4} = {3}
It is denoted as “A - B”

4.Set Complement:

The set complement is the list of all elements present in the Universal set except the elements present in set A
It is denoted as “U-A”

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are

The Correct Option is B

Solution and Explanation

Top Questions on Operations on Sets

Notes on Operations on Sets

Concepts Used:

Operations on Sets

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