Q. 50

Fill in the blanks

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then

(i) (B C)′ is ______________.

(ii)(C – A)′ is ______________.

Answer :

(i) {1, 5, 9, 10} (ii) {1, 2, 3, 5, 6, 7, 9, 10}


Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}


To find: (B C)′ and (C – A)′


Formula used:


The union of two sets is a set containing all elements that are in both sets.


For example: {1, 2, 3} {2, 4} = {1, 2, 3, 4}


The difference (subtraction) is defined as: The set A – B consists of elements that are in A but not in B.


For example: if A = {1, 2, 3} and B = {3, 5}, then A−B = {1, 2}


B = {2, 4, 6, 7} and C = {2, 3, 4, 8}


B C = {2, 3, 4, 6, 7, 8}


(B C)’ = U – (B C)


= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {2, 3, 4, 6, 7, 8}


= {1, 5, 9, 10}


A = {1, 2, 3} and C = {2, 3, 4, 8}


C – A = {4, 8}


(C – A)’ = U – (C – A)


= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {4, 8}


= {1, 2, 3, 5, 6, 7, 9, 10}


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RELATED QUESTIONS :

If and x < 8}, and B = , find :

(i) A B


(ii) A B


(iii) A – B


(vi) B – A


RS Aggarwal - Mathematics