DeMorgans Laws...Sets of numbers and its complements.

Question

Let U= {1,2,3,4,5,6,7,8,9,10,a,b,c,d,e}. If A={1,2,a,e} and B={1,2,3,4,a,b,c}, find the following.

a.) n(A^c)

b.) n(A ∩ B^c)

c.) n(A ∪ B^c)

d.) n(A^c ∩ B^c)

Thank you so much in advance!

Answer 1

Hello, B! I would be more than happy to assist you with this problem!

a.) n(A^c) = The number of elements that are in the universal (U), but not in set A.

b.) n(A ∩ B^c) = The number of elements shared by those in set A and those not in set B.

c.) n(A ∪ B^c) = The number of elements from set A and those that are not in set B, put together. Do not repeat any elements.

d.) n(A^c ∩ B^c) = The number of elements that are shared by those not in set A and those not in set B, from the universal (U).

In other words, indicate how many elements there are for parts a, b, c, and d.