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Advanced MathQ&A LibraryFor problems 1 through 11, use the following sets. The set U is the universal set.0- -32, - 8, -2, - 3, 1, 4, 16, 64)N-1,2,4,8)U= {-32,-8,-2, .. 1, 2, 100-, 8. 1004. 10003, 64)S-2245, 1000,, B16)1. Write set B in roster notation.2. Write set O in set-builder notation3. Write the number of subsets of N in binary4. Write the number of proper subsets of U in hexidecimal.5. Convert each element of S to base-ten (decimal)6. How many two-way intersections of the sets B. O. N u. and S exist? (e.g. Nno, ons, etc)7. If -47Question

Asked May 13, 2019

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I need the explanation for number 6 and 7

Step 1

- The sets are given as
*B, O, N, U, S*in which*U*is the Universal set.

In order to find the number of two-way intersections like (*N∩B, O∩U*, etc.) of the sets *B, O, N, U, S*, obtain the permutations as first place has 5 choices and second place will have 4 choices.

Step 2

The number of two-way intersection of the sets *B, O, N, U, S* is 10. However, out of 10, only 6 intersections are possible that are *U∩B, U∩O, U∩N, N∩B, N∩O*, and *O∩B*.

Step 3

Set *S* has no intersection with any other set as the elements are the numbers with some bases that do not even matches wit...

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