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Check whether the following sets are equ...

Check whether the following sets are equivalent ?
(i) A = {x : x is a letter in the word SOLUTION} B = {P, R, O, B, L, E, M}
(ii) C = {x : x is either or composite, `x lt 10`}
`D={1}`

Text Solution

Verified by Experts

The correct Answer is:
(i) Yes (ii) No
(a) `A={S, O, L, U, T, I, N}`
`n(A)=7`
`B={P, R, O, B, L, E, M}`
`n(B)=7`
Since `n(A)=n(B)`,
`:. A` and B are equivalent sets.
(b) `C-{x : x in N, x" is either prime or composite"}` i.e., `C` is the collection of all natural numbers except 1, less than 10.
`C={2, 3, 4, 5, 6, 7, 8, 9}`
`n(C)=8`
`D={1}`
`n(D)=1`
Since `n(C) ne n(D)`,
`:. C` and `D` are not equivalent sets.
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