Okay, let's break this down step-by-step:
U = x < 20, x is a natural number
A = x
B = 1 < x < 15
C = x is an odd number, x is a natural number
(a) A n B' (using De Morgan's law: A n B' = A' U B')
= x
= {16, 17, 18, 19}
(b) B C' U A
= B U (C' U A)
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} U {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14}
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
(c) (A' n C ')
= (A' C') (by De Morgan's law)
= x
= {16, 18}
The Venn diagram would be:
U A B C
_____|_____|_____|_____
| | | |
| | | |
| | ___|_____|___
| | | |
| | | 16, 17, 18, 19
| | | |
| | |_____|_____|___
| | | | |
| | | ___|_____|___
| | | | 16, 18
| | | |_____|_____|___
Does this make sense? Let me know if you have any other questions!