(Q2) Given that Y={multiples of 3 less than 20}, find the number of proper subsets of Y?
90
To find the number of proper subsets of Y, we can use the formula 2^n - 1, where n is the number of elements in the set.
In this case, the set Y contains the multiples of 3 less than 20. Let's list these multiples:
Y = {3, 6, 9, 12, 15, 18}
To find the number of proper subsets, we need to find the number of elements in Y, which is 6.
Using the formula 2^n - 1, we can calculate:
2^6 - 1 = 64 - 1 = 63
Therefore, the number of proper subsets of Y is 63.
To find the number of proper subsets of Y, we first need to understand what a proper subset is. A proper subset of a set is a subset that does not contain all the elements of the original set.
In this case, the set Y is defined as the set of multiples of 3 less than 20. We need to find the number of proper subsets of Y.
To calculate the number of proper subsets of a set, we can use the formula 2^n - 1, where n is the number of elements in the set. In this case, the number of elements in the set Y is the number of multiples of 3 less than 20.
To find the number of multiples of 3 less than 20, we can list them out:
3, 6, 9, 12, 15, 18
So, the set Y consists of 6 elements. Applying the formula, we can calculate the number of proper subsets:
2^6 - 1 = 64 - 1 = 63
Therefore, there are 63 proper subsets of the set Y.