Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Two Finite Sets Have M and N Elements. the Number of Elements in the Power Set of First Set is 48 More than the Total Number of Elements in Power Set of the Sec - Mathematics

MCQ

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:

•  7, 6

•  6, 3

• 7, 4

• 3, 7

#### Solution

6, 4

ATQ : $2^m - 1 = 48 + 2^n - 1$
$\Rightarrow 2^m - 2^n = 48$
$\Rightarrow 2^m - 2^n = 2^6 - 2^4$
$\text{ By comparing we get }:$
$m = 6 \text{ and } n = 4$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Q 24 | Page 51