two finite sets have m and n elements the total number if sub sets of the first set is 12 more than the total number of subsets of the second set. find the value of m and n. ( plz answer this question).
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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.
Step-by-step explanation:
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