2 finite sets have 'm' and 'n' elements . The number of subsets of first is 48 more than the number of subsets of second set .Then what is m and n
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The number of subsets of the first set is 112more than that of the second set. Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively, (a) 4,7 (b) 7,4 (c) 4,4 (d) 7, 7
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Step-by-step explanation:
Let A has m elements
Let B has n elements
Total number of students of A=2m
Total number of students of B=2n
It is given ⇒2m−2n=56
2n(2m−n−1)=56
⇒2n=even and 2m−n−1=0 odd
Now,
56=8×7=23×27
⇒2n(2m−n−1)=23×7
⇒n=3
Now, 8(2m−3−1)=8×7
⇒2m−3−1=7
⇒2m−3=8=23
⇒m−3=3
⇒m=6.
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