Question

Determine the number of proper subsets contained in T if T={x∣∣xis an odd, negative integer andx>−12}.

Answer 1

In order to find the number of proper subsets contained in T, we first need to determine the number of elements in the set T.

Since T is a set of odd, negative integers greater than -12, we can list out the elements in T:
T = {-11, -9, -7, -5, -3, -1}

There are 6 elements in the set T.

Now, we know that for a set with n elements, the number of proper subsets is given by 2^n - 1. Therefore, the number of proper subsets in T is:
2^6 - 1 = 64 - 1 = 63

So, there are 63 proper subsets contained in the set T.