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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)
(iii) {0,1,2,3,4,5,6,7,8,9,10}
(iv) {1,2,3,4,5,6,7,8}
Answers (1)
All the sets A,B,C are subsets of universal set .
Consider (i) {0, 1, 2, 3, 4, 5, 6} as universal set .
A {0, 1, 2, 3, 4, 5, 6} and B
{0, 1, 2, 3, 4, 5, 6} but C
{0, 1, 2, 3, 4, 5, 6}.
Hence, {0, 1, 2, 3, 4, 5, 6} is not universal set.
Consider (ii) as universal set..
A ,B
and C
.
Hence, is not universal set.
Consider (iii){0,1,2,3,4,5,6,7,8,9,10} as universal set.
A {0,1,2,3,4,5,6,7,8,9,10},B
{0,1,2,3,4,5,6,7,8,9,10} and C
{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.
A {1,2,3,4,5,6,7,8}, B
{1,2,3,4,5,6,7,8} BUT C
{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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