Question

List all the elements of the following sets :

(i) A = {x : x is an odd natural number}

(ii) B = (x: x is an integer, 1212 < x < 9292

(iii) C = (x : x is an integer, x² ≤ 4}

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

(v) E = ( x : x is a month of a year not having 31 days}

(vi) F = (x: x is a consonant in the English alphabet which precedes k}

Answer 1

(i) A = { x : x is an odd natural number}

We know that 1, 3, 5, 7, 9, 11 are infinite odd natural numbers. So, listed form of above set will be A = {1, 3, 5, 7, 9, 11,....}

(ii) B = {x: x is an integer \(\frac{1}{2} < x < \frac{9}{2}\)}

We know that 0, 1,2, 3, and 4 are integers between \(-\frac{1}{2} \ and \ \frac{9}{2}\) as shown on number line.

Thus, B = { 0,1,2,3,4} is listed form of given set B.

(iii) C = {x: x is an integer, x2 < 4}

We see that square of any integer which is equal to or less than 4 is as follows : (-2)² =4, (-1)² =1, 0² = 0 1² = 1, 2² = 4

We see that integers having square as 4 or less than 4 are -2, - 1, 0, 1 and 2.

Thus, list form of set C will be as follows : C = {-2, -1, 0, 1, 2}

(iv) D = {x: x is a letter in the word ‘LOYAL’}

In word LOYAL, L is repeated two times so list form of given set will be

D = {L, O, Y, A}

(v) We know that months of the year not having 31 days are Feb, April, June, Sep, Nov

Thus, given set in listed from will be

E = {Feb, April, June, Sep, Nov}

(vi) Letters of English alphabet which occurs before K are a, b, c, d, e,f g, h, i ,j out of which b, c, d, f, g, h, 7 are constants so listed form is :

{b, c, d, f, g, h, j}

⇒ Set F= {b, c, d, fg, h, j}