Q.9 Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C

(i) {0, 1, 2, 3, 4, 5, 6} 

(ii)  \phi

(iii) {0,1,2,3,4,5,6,7,8,9,10}

(iv) {1,2,3,4,5,6,7,8}

Answers (1)
S safeer

All the sets A,B,C are subsets of universal set .

Consider (i) {0, 1, 2, 3, 4, 5, 6}  as universal set .

                 A \subset  {0, 1, 2, 3, 4, 5, 6} and B \subset {0, 1, 2, 3, 4, 5, 6} but C \not\subset  {0, 1, 2, 3, 4, 5, 6}.

Hence, {0, 1, 2, 3, 4, 5, 6} is not universal set.

Consider (ii) \phi as universal set..

               A \not\subset\phi,B \not\subset\phi and C \not\subset\phi.

Hence,\phi is not universal set.

Consider (iii){0,1,2,3,4,5,6,7,8,9,10} as universal set.

 A\subset {0,1,2,3,4,5,6,7,8,9,10},B\subset{0,1,2,3,4,5,6,7,8,9,10} and C \subset {0,1,2,3,4,5,6,7,8,9,10}

Hence, {0,1,2,3,4,5,6,7,8,9,10} is universal set.

Consider (iv){1,2,3,4,5,6,7,8} as universal set.

\subset {1,2,3,4,5,6,7,8}, B \subset {1,2,3,4,5,6,7,8} BUT C \not\subset {1,2,3,4,5,6,7,8}.

Hence,{1,2,3,4,5,6,7,8} is not universal set.

Answer is (iii){0,1,2,3,4,5,6,7,8,9,10}.

 

 

 

 

 

 

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