Question

two finite sets have m and n ekements respectively. the total number of subsets of first set is 56 more than the total number of subsets of the second set. the values of m and n respectively are a 7,6 b 5,1 c 6,3 d 8,7

Answer 1

Step-by-step explanation:

ANSWER

Let A has m elements

Let B has n elements

Total number of students of A=2

m

Total number of students of B=2

n

It is given ⇒2

m

−2

n

=56

2

n

(2

m−n

−1)=56

⇒2

n

=even and 2

m−n

−1=0 odd

Now,

56=8×7=2

3

×2

7

⇒2

n

(2

m−n

−1)=2

3

×7

⇒n=3

Now, 8(2

m−3

−1)=8×7

⇒2

m−3

−1=7

⇒2

m−3

=8=2

3

⇒m−3=3

⇒m=6.