Let `U={1,2,3,4,5,6,7,8,9}, A={1,2,3,4},B={2,4,6,8} and C={3,4,5,6}` Find :
(i) `A'`
(ii) `B'`
(iii) `(A cup C)'`
(iv) `(A cap B)'`
(v) `(A')'`
(vi) `(B-C)'`.

Answer

A=B

Explanation

U={1,2,3,4,5,6,7,8,9}
A = (1,2,3, 4},B= {2, 4, 6, 8}, C= {3, 4, 5, 6}
(a) A'={5,6,7,8,9,}
(b) B'={1,3,5,7,9}
( c) `A cup C` = {1,2,3,4,5,6}
`therefore ( A cup C )'={7,8,9}`
(d) `(A cup B) = {1,2,3,4,5,6,8}
` therefore ( A cup B )' = { 5,7,9}
(e) ( A') = A= { 1,2,3,4}
(f) B-C = { 2,8}
`therefore ( B- C)'={ 1,3,4,5,6,7,9}