Compute A^c – B and draw a Venn diagram.

Given that

`U = {xIx \in W, \le x \le 20}`
`A = {x \in P, x \le 20}`
`B = {x \in N, x \le 15}`
Where P is the set of prime numbers and N is the set of Natural Numbers
Compute `A^c – B` and draw a Venn diagram.

Solution:

Here

U = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
A={2,3,5,7,11,13,17,19}
B={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
First, we compute `A^c`
`A^c` = U – A = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} - {2,3,5,7,11,13,17,19}
= {0,4,6,8,9,10,12,14,16,18,20}
Now we compute `A^c – B`
`A^c – B` = {0,4,6,8,9,10,12,14,16,18,20} - {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
={0,16,18,20}

Venn diagram