Q8 of 71 Page 14

Which of the following sets are equivalent?

i.


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


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


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.


More from this chapter

All 71 →
6

Find the cardinal number of the following sets

i.


ii. B = {x : x is a consonant in English Alphabet}


iii. X = {x: x is an even prime number}


iv.


v.

7

Identify the following sets as finite or infinite

i. A = {4, 5, 6, ...}


ii. B = {0, 1, 2, 3, 4, ... 75}


iii. X = {x : x is an even natural number}


iv. Y = {x : x is a multiple of 6 and x > 0}


v. P = The set of letters in the word ‘freedom’

 9

Which of the following sets are equal?

i. A = {1, 2, 3, 4}, B = {4, 3, 2, 1}


ii. A = {4, 8, 12, 16}, B = {8, 4, 16, 18}


iii. X = {2, 4, 6, 8}


Y = {x : x is a positive even integer 0 < x < 10}


iv. P = {x : x is a multiple of 10, }


Q = {10, 15, 20, 25, 30, ...}

 10

From the sets given below, select equal sets.

A = {12, 14, 18, 22}, B = {11, 12, 13, 14}, C = {14, 18, 22, 24}


D = {13, 11, 12, 14}, E = {−11, 11}, F = {10, 19}, G = {11, −11}, H = {10, 11}