Question

two finite sets have m and n elements the number of subsets of the first set is 96 more then find m+n​

Answer 1

Answer:

Two finite sets have m and n elements. If the total number of subsets of first set is 56 more than the total number of subsets of second set, then find the values of m and n.

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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.

Answer 2

It had an area of 880 square kilometres at the beginning of the 20th century, but having lost significantly to erosion it covers 553 square kilometres as at 2014