Sets

12. B = D = {1, 2, 3, 4} = {3, 1, 4, 2}

E = G = {–1, 1} = {1, –1}.

11. (i) A = {2, 3)

B = {x : x is solution of x² + 5x + 6 = 0}

So, x² + 5x + 6 = 0

x² + 2x + 3x + 6 = 0

x (x+2) + 3 (x+2) = 0

(x+2) (x+3) = 0

x = –2, –3

So, B = {–2, –3}

So, A ≠ B.

(ii) A = {x : x is a letter in word FOLLOW}

A = {F, O, L, W}

(iii) B = {x : x is a letter in word WOLF}

B = {W, O, L, F}

So, A = B as the elements are all same.

10. (i) As A and B has a, b, c and d as elements and are exactly the same, Hence, A = B.

(ii) Hence, 12 $\in$ A but 12 $\notin$ B

Similarly 18 $\in$ B but 18 $\notin$ A.

So, A ≠ B.

(iii) A = {2,4,6,8,10} and B = {2,4,6,8,10}

So, A=B.

(iv) A= {10,20,30,40, …} and B= {10,15,20,25,30, …}

So, A ≠ B.

9. (i) We can draw infinite number of lines parallel to x-axis.

∴ The set is infinite.

(ii) There are 26 letters in the English alphabet.

∴ The set is finite.

(iii) There are infinite number which are a multiple of 5.

∴ The set is infinite

(iv) The numbers of animals living on earth are finite.

∴ The set is finite.

(v) There can be infinite number of circular passing through origin (0,0).

∴ The set is infinite.

8. (i) The set of months of a year has 12 elements. Here, the set is finite.

(ii) The given set has the natural number as its elements. Hence, the set is infinite.

(iii) The given set has 100 elements i.e., from 1 to 100. Hence, the set is finite.

(iv) There are infinite numbers of positive integers greater than 100. Hence the set is infinite.

(v) The numbers of prime number less than 99 is finite. Hence, the set is finite.

1. (i) There is no odd number that can be divided by 2.

?The given set is a null set.

(ii) An even prime number is 2. Hence, the set will have 2 as element.

? The given set is not a null set.

(iii) As there is no natural number which is both less than 5 and greater than 7.

? The given set is a null set.

(iv) Two parallel lines never meets and hence no common point.

? The given set is a null set.

6. (i) (c)

(ii) (a)

(iii) (d)

(iv) (b)

5. (i) A = {1, 3, 5, 7, …}

(ii) B = {0,1,2,3,4} (as $\frac{9}{2}$ =4.5 and $-\frac{1}{2}$ = –0.5)

(iii) x² ≤ 4

x² ≤ 2²

x ≤ ± 2

So, C = {–2, –1,0,1,2}

(iv) D = {L, O, Y, A}

(v) E = {February, April, June, September, November}

(vi) F = {b, c, d, f, g, h, j}

4. (i) {3,6,9,12}= {3 * 1, 3 * 2, 3 * 3, 3 * 4}

= {x : x = 3n, n is natural number and 1≤ n ≤ 4}

(ii) {2,4,8,16,32}= {2¹, 2², 2³, 2⁴, 2⁵}

= {x : x = 2ⁿ, n is natural number and 1 ≤ n ≤ 5}

(iii) {5,25,125,625}= {5¹, 5², 5³, 5⁴}

= {x : x = 5ⁿ, n is natural number and 1 ≤ n ≤ 4}

(iv) {2,4,6, }= {2 * 1, 2 * 2, 2 * 3, …}

= {x : x = 2n, n is a natural number}

(v) {1,4,9, …, 100}= {1², 2², 3², …, 10²}

= {x : x = n2, x is a natural number and 1 ≤ n ≤ 10}