Answer :

i. A = {2, 4, 6, 8, 10}

∴ n(A) = 5

B = {1, 3, 5, 7, 9}

∴ n(B) = 5

∴ n(A) = n(B)

∴ A ≈ B [≈ → equivalent]

ii. X = {x : x∈N, 1<x<6}

∴ The possible values of x : 2, 3, 4, 5

∴ X = {2, 3, 4, 5}

∴ n(X) = 4

Y = {x : x is a vowel in the English Alphabet}

∴ Y = {a, e, i, o, u}

∴ n(Y) = 5

∴ n(X) ≠ n(Y)

∴ The sets X and Y are not equivalent.

iii. P = {x : x is a prime number and 5 < x < 23}

The prime numbers between 5 and 23 are: 7, 11, 13, 17, 19

∴ P = {7, 11, 13, 17, 19, 21}

∴ n(P) = 6

Q = {x : x∈W, 0≤x<5}

∴ The possible values of x : 0, 1, 2, 3, 4

∴ Q = {0, 1, 2, 3, 4}

∴ n(Q) = 5

∴ n(P) ≠ n(Q)

∴ The sets P and Q are not equivalent.

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