Question

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}`.

Answer 1

Let `A = {1,3,5}`
`B = {2,4,6}`
`C= {0,2,4,6,8}`
The set in which the elements of three sets are included `={0,1,2,3,4,5,6,8}`
Here, in option (iii), there are all those elements which are in A,B or C along with some other elements
Therefore, set `{0,1,2,3,4,5,6,7,8,9,10}` given in option (iii) is the universal set.