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In the following, state whether A = B o...

In the following, state whether A = B or not :
(i) `A = {a,b,c,d}`
`B = {d,c,b,a}`
(ii) `A = {2,4,6,8,10}`
B = {x : x is positive even integer and `x le 10`}
(iii) A = {x : x is a multiple of 10}
`B ={10,15,20,25,30,...}`.

Text Solution

Verified by Experts

(i) `because A = {a,b,c,d} and B ={d,c,b,a}`
Here, each element of set A is in set B and each element of B is in A
Therefore, A = B
(ii) `becauseA={4,8,12,16}andB={8,4,16,18}`
Here the element 12 of set A is not in set B
Therefore, `A ne B`
(iii) `because A = {2,4,6,8,10}`
and B = {x : x is positive even integer and `x le 10`}
`={2,4,6,8,10}`
Therefore, A = B
(iv) `because` A = {x : x is a multiple of 10}
`={10,20,30,40,50,...}`
`B = {10,15,20,25,30,...}`
Here, the elements 15,25,... etc, of set B are not in set A therefore `A ne B`.
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