Q. 1 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 \cup B)′

(v) (A')'

(vi) (B – C)'

Answers (1)

 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 }

(i) A′ = U - A = {5,6,7,8,9}

(ii) B′ = U - B = {1,3,5,7,9}

(iii) A \cup C = {1,2,3,4,5,6}

     (A \cup C)′ = U - (A \cup C) = {7,8,9}

(iv) (A \cup B) = {1,2,3,4,6,8}

      (A \cup B)′ = U - (A \cup B) = {5,7,9}

(v) (A')' = A = { 1, 2, 3, 4}

(vi) (B – C) = {2,8}

       (B – C)' = U - (B – C) = {1,3,4,5,6,7,9}

 

 

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