Question

5. Let U = (x/x is less than 20, x €

N] and let A = (x/3 < x < 15), B =
(x/1 < x < 15) and C (x/x is an odd
number, x € Llj Carry out the
following operations and make
the Venn diagram
(a) AnB'
(B C'UA
(the bac
[d) (A'nc')

Answer 1

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!