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}

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.

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