Two sets A and B contains a and b elements respectively. If power set of A contains 16 more elements than that of B, value of ‘b’ and ‘a’ are _______a.4, 5b.2, 3c.None of the mentionedd.6, 7
Question
Two sets A and B contains a and b elements respectively. If power set of A contains 16 more elements than that of B, value of ‘b’ and ‘a’ are _______a.4, 5b.2, 3c.None of the mentionedd.6, 7
Solution
The number of elements in a power set is given by 2^n, where n is the number of elements in the original set.
So, the power set of A has 2^a elements and the power set of B has 2^b elements.
According to the problem, the power set of A has 16 more elements than the power set of B.
So, we can write the equation as:
2^a = 2^b + 16
We can solve this equation by trying different values of a and b.
If we try a=5 and b=4, we get:
2^5 = 2^4 + 16
32 = 16 + 16
32 = 32
So, the values of a and b that satisfy the equation are a=5 and b=4.
Therefore, the correct answer is a. 4, 5.
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