Q6 of 23 Page 30

Write the following sets in the set-builder form.

(i) {3, 6, 9, 12}


(ii) {2, 4, 8, 16, 32}


(iii) {5, 25, 125, 625}


(iv) {1, 4, 9, 16, 25 … 100}

We know that when we write a set by defining its elements with a “common property”, we can say that the set is in set builder form.


(i) {3, 6, 9, 12}


⇒ 3, 6, 9, 12 are the multiples of 3 and they are less than 13.


∴ A={x: x is multiple of 3 & less than 13}


(ii) {2, 4, 8, 16, 32}


⇒ Here 2, 4, 8, 16, 32 are in the form of 21, 22, 23, 24, 25


Where 1, 2, 3, 4, 5 are the powers of 2 and power is less than 6.


∴ B = {x: x is a power of 2x & x is less than 6}


(iii) {5, 25, 125, 625}


⇒ Here 5, 25, 125, 625 are in the form of 51, 52, 53, 54.


Where 1, 2, 3, 4 are the powers of 5 and power is less than 5.


∴ C = {x: x is a power of 5 & x is less than 5}


(iv){1, 4, 9, 16, 25 … 100}


⇒ Here 1, 4, 9 16, 25 … 100 are in the form of 12, 22, 32, 42, 52 … 102 where 1, 2, 3, 4, 5 … 10 are natural numbers and the given numbers are squares and not greater than 10.


∴ D = {x : x in square of natural number and not greater than 10}


More from this chapter

All 23 →
4

State whether the following statements are true or false. Justify your answer

(i) 5 set of prime numbers


(ii) S = {5, 6, 7} implies 8 ∈S.


(iii) -5 W where ‘W’ is the set of whole numbers


(iv) Z where ‘Z’ is the set of integers.

 5

Write the following sets in roster form.

(i) B = {x : x is a natural number smaller than 6}


(ii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}.


(iii) D = {x : x is a prime number which is a divisor of 60}.


(iv) E = {x : x is an alphabet in BETTER}.

 7

Write the following sets in roster form.

(i) A = {x : is a natural number greater than 50 but smaller than 100}


(ii) B = {x : x is an integer, x2 = 4}


(iii) D = {x : x is a letter in the word “LOYAL”}

 8

Match the roster form with set builder form.

(i) {1, 2, 3, 6}


(ii) {2, 3}


(iii) {M, A, T, H, E, I, C, S}


(iv) {1, 3, 5, 7, 9}


(a) {x : x is prime number and a divisor of 6}


(b) {x : x is an odd natural number smaller than 10}


(c) {x : x is a natural number and divisor of 6}


(d) {x : x is a letter of the word MATHEMATICS}