sets word problem

Question

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}

A = {1, 2, 4, 5}

B = {1, 3, 5, 7}

How many elements are in (A ∪ B')' ?

Answer 1

U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5}
B = {1, 3, 5, 7}

 

B' = U - B = {1, 2, 3, 4, 5, 6, 7} - {1, 3, 5, 7} = {2, 4, 6}

 

A U B' = {1, 2, 4, 5} + {2, 4, 6} = {1, 2, 4, 5, 6}

 

(A U B')' = U - (A U B') = {1, 2, 3, 4, 5, 6, 7} - {1, 2, 4, 5, 6} = {3, 7}

 

Set (A U B')' contains two elements, {3, 7}