Two finite sets have x and y number ofelements. The total number of subsets ofthe first set is four times the total numberof subsets of second set. Find out the valueof x —
Question
Two finite sets have x and y number ofelements. The total number of subsets ofthe first set is four times the total numberof subsets of second set. Find out the valueof x —
Solution
The number of subsets of a set with n elements is 2^n.
Given that the total number of subsets of the first set is four times the total number of subsets of the second set, we can write the equation:
2^x = 4 * 2^y
Solving for x, we get:
2^x = 2^2 * 2^y
Since the bases are the same, we can equate the exponents:
x = 2 + y
So, the value of x is y + 2.
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