Consider the following sets:
A= set ofnaturai numbers which are multiples of 2
B= set ofnaturai numbers which are multiples of 3
C= set ofnaturai numbers which are multiples of 5
Then find the following set
`(i) A cup B (ii) B cup C (iii) A- B (iv) B-C (v)A cap C
(vi) A cap B cap C (vii) ( A cup B )- C`

Explanation

We have
A a set of natural numbers which are multiples of 2 M
B = set of natural numbers which are multiples of 3
C = set of natural numbers which are multiples of 5
` A cup B` = set of natural numbers which are multiples of 2 or 3
= { 3,5,6,9,10,12,15,18,20....}
A- B = {2,4,6,8,10,12,14,16,18,....}
- {3,6,9,12,15,18....}
= set of natural numbers Which are multiples of 2 but not multiples of 3 z: {2, 4, 8,10,14,16, 20, ...}
In this set, elements 6, 12, 18, . . . are excluded which are multiples of 2 and 3 both.
Similarly
B-C= {3, 6, 9,12,15,18, 21, 24, 27, 30, ...}
- {5,10,15, 20, 25, 30, ...}
= {3, 6, 9,12,18, 21, 24, 27, 33, ...}
In this set, elements 15, 30, . .. are excluded which are multiples of 3 and 5 both. `A cap B` = set of natural numbers which are multiples of 2 and 5 both
= set of natural numbers Which are multiples of 10 = {10, 20, 30, 40, 50, . ..}
`A cap B cap C` . = set of naturanl hmbers whicha re multiples a 2, 3 and 5
= set of natural numbers which are multiples of 30
= {30, 60, 90, 120, 150, ...} `(A cup B)- C ` = set of natural numbers which are muldplwi 2 or 3 but not 5
= {2, 3, 4, 6, 8, 9,12,14,16,18, 21, ...} In this set, elements 5, 10, 15, 20, 25, 30, are excluded.