Given that Y={multiples of 3 less than 20}, find the number of proper subsets of Y?
Well, let me put on my mathematician clown hat for this one!
To find the number of proper subsets of Y, we can use a little trick. Since Y consists of multiples of 3 less than 20, let's look at the number of elements in Y first.
The largest multiple of 3 less than 20 is 18. So we can say that Y has 18 divided by 3 plus 1 elements, which is 6 elements.
Now, for any set with n elements, the number of proper subsets is given by 2^n - 1. Since Y has 6 elements, the number of proper subsets is 2^6 - 1, which is 63.
So, there are 63 proper subsets of Y. And that's no joke!
To find the number of proper subsets of set Y, we need to understand that a proper subset is a subset that does not include the entire set.
The set Y consists of the multiples of 3 less than 20, which are {3, 6, 9, 12, 15, 18}.
To find the number of proper subsets, we can use the formula 2^n, where n is the number of elements in the set.
In this case, the set Y has 6 elements, so the total number of subsets (including the empty set and the set itself) is 2^6 = 64.
To find the number of proper subsets, we subtract 2 from the total number of subsets:
64 - 2 = 62
Therefore, there are 62 proper subsets of the set Y.
To find the number of proper subsets of Y, we need to first determine the number of elements in Y.
Y is defined as the set of multiples of 3 less than 20. To find all the multiples of 3 less than 20, we can start by dividing 20 by 3:
20 ÷ 3 = 6 remainder 2
This tells us that the largest multiple of 3 less than 20 is 18. Therefore, the elements of Y are {3, 6, 9, 12, 15, 18}.
Now we can calculate the number of proper subsets of Y. A proper subset is a subset that contains at least one element, but not all of the elements.
To count the number of proper subsets, we can use the formula 2^n - 1, where n represents the number of elements in the set.
In this case, Y has 6 elements. So, 2^6 - 1 gives us:
2^6 - 1 = 64 - 1 = 63
Therefore, there are 63 proper subsets of Y.