Sets

18. (i) As x does not include –4 while 6 is included.

(–4, 6].

(ii) As x does not include both –12 and –10.

(–12, –10)

(iii) As x includes 0 but does not includes 7.

[0, 7)

(iv) As includes both 3 and 4

[3, 4]

17. As A= $?$ , no elements

n(A) = 0 = m

So, n[P(A)] = 2^m = 2⁰ = 1.

16 (i) Subset of {a} = {a}, $?$ .

(ii) Subset of {a, b} = $?$ ,{a},{b},{a, b}

(iii) Subset of {1,2,3} = $?$ ,{1},{2},{3}, {1,2}, {1,3}, {2,3}, {1,2,3}.

(iv) Subset of $?$ = $?$ .

15. (i) False as 3 $\notin$ A and 4 $\notin$ 4. So, {3, 4} $\cancel{\subset }$ A.

(ii) True as {3, 4} $\in$ A. i.e, {3, 4} is an element of A.

(iii) True as {3, 4} $\in$ A so, {3, 4} $\subset$ A.

(iv) True as 1 is an element of A.

(v) False as 1 is not a set so it cannot be a subset of A.

(vi) True as 1 $\in$ A, 2 $\in$ A and 5 $\in$ A. so, {1, 2, 5} $\subset$ A.

(vii) False as {1, 2, 5} is not an element of A.

(viii) False of 3 $\notin$ A.

(ix) False as $?$ is not an element of A.

(x) True, $?$ ? A as $?$ is a subset of every set.

(xi) False, as $?$ is not an element of A.

14. (i) False as every element of set {a, b} is also an element of {b, c, a} hence {a, b } $\subset$  { b, c, a }.

(ii) True as every element in {a, e} is also a vowel in English alphabet.

(iii) False as 2 $\in$  {1, 2, 3} but 2 $\notin$  {1, 3, 5}.

(iv) True as a $\in$  {a} is also a $\in$  {a, b, c}

(v) False as a $\in$  {a, b, c} but {a} $\in$  {a, b, c}

(vi) {x : x is an even natural number less than 6} = {2, 4}

{x : x is a natural number which divides 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36}

As {2, 4} $\subset$  {1, 2, 3, 4, 6, 9, 12, 18, 36}

It is true.

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.