Question

Let U = {0, 1, 2 , 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets.

(i) A’
(ii) B’
(iii) A ‘ $\cup$ B’
(iv) A’ $\cap$ B’
(v) (A $\cup$ B)’
(vi) (A $\cap$ B)’
(vii) (A’)’
(viii) (B’)’

Answer 1

(i) A’ = U – A = {0, 1 ,2, y, 4, 5, 6, 7} – {1, 3, 5, 7} = {0, 2, 4, 6}

(ii) B’ = U – B = {0, 1, 2, 3, 4, 5, 6 ,7} – {0, 2, 3, 5, 7} = {1, 4, 6}

(iii) A’ $\cup$ B’ = {0, 2, 4, 6} $\cup$ {1, 4, 6} = {0, 1, 2, 4, 6}
(iv) A’ $\cap$ B’ = {0, 2, 4, 6} $\cap$ {1, 4, 6} = {4, 6}

(v) (A $\cup$ B)’ = U – (A $\cup$ B) = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 1, 2, 3, 5, 7} = {4, 6}

(vi) (A $\cap$ B)’ = U – (A $\cap$ B)= {0, 1, 2, 3, 4, 5, 6, 7} – {3,5,7} = {0, 1, 2, 4, 6}

(vii) (A’)’ = U – A’ = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 2, 4, 6} = {1, 3, 5, 7}

(viii) (B’)’ = U – B’ = {0, 1, 2, 3, 4, 5, 6, 7} – {1, 4, 6} = {0, 2, 3, 5, 7}.