the total number of subsets of a finite set a has 56 more elements than the total no of subset of another finite set b. what is the no of elements in set a.
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Answered by
15
Let the number of elements in set A be p and set B be q.
The power set of A is P (A) and B is P (B).
P (A) has 2p elements and P (B) has 2q elements.
2p – 2q = 56
2q [2p-q – 1] = 8 * 7 = 23 [23 – 1]
2q [2p-q – 1] = 23 [23 – 1]
q = 3, p – q = 3
p – 3 = 3
p = 3 + 3 = 6
Answered by
2
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.
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