Let U = {0, 1, 2 , 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3,

1.	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‘ ∪ B’(iv) A’ ∩ B’(v) (A ∪ B)’(vi) (A ∩ B)’(vii) (A’)’(viii) (B’)’
Answer» (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’ ∪ B’ = {0, 2, 4, 6} ∪ {1, 4, 6} = {0, 1, 2, 4, 6} (iv) A’ ∩ B’ = {0, 2, 4, 6} ∩ {1, 4, 6} = {4, 6} (v) (A ∪ B)’ = U – (A ∪ B) = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 1, 2, 3, 5, 7} = {4, 6} (vi) (A ∩ B)’ = U – (A ∩ 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}.

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‘ ∪ B’(iv) A’ ∩ B’(v) (A ∪ B)’(vi) (A ∩ B)’(vii) (A’)’(viii) (B’)’

Answer»

(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’ ∪ B’ = {0, 2, 4, 6} ∪ {1, 4, 6}

= {0, 1, 2, 4, 6}

(iv) A’ ∩ B’ = {0, 2, 4, 6} ∩ {1, 4, 6} = {4, 6}

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

= {4, 6}

(vi) (A ∩ B)’ = U – (A ∩ 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}.