Chapter 1: Sets – Exercise 1.3
Sets – Exercise 1.3 – Q.1
(i) This set is non-empty as 10 is an even natural number divisible by 5.
(ii) As 2 belongs to this set, so it is non-empty.
(iii) 
the set of rational numbers So, this set is empty.
(iv) This set is empty as there is no natural num bar x such that x < 8 and simultaneously x > 12.
(v) This set is empty as any two parallel lines never intersect each other.
Sets – Exercise 1.3 – Q.2
(i) Infinite, since with a common centre infinitely many circles can be drawn in a plane.
(ii) Finite, as there are only 26 letters of English Alphabet.
(iii) Infinite, ∵ {x ϵ N : x > 5} = {6,7,8,...} which is infinite.
(iv) Finite, ∵ {x ϵ N : x ,200} = {1,2, 3,...199} Which is finite.
(v) Infinite, {x ϵ Z : x < 5} =-{...., -3,-2,-1,0,1,2,3,4,} Which is infinite,
(vi) {x ϵ R : 0 < x < 1) is an infinite set ∵ an interval is an infinite set.
Sets – Exercise 1.3 – Q.3
A = {1,2,3}
B = {x ϵ R : (x - 1)2 = 0}
= {x ϵ R : x = 1,1}
= {1}
C = {1,2,3} (∵ repetition is not allowed in a set)
D = {x ϵ R : x3 - 6x2 + 11x - 6 = 0}
= {x ϵ R : (x- 1)(x2- 5x + 6) = 0} [∵ x = 1 satisfiles the above equation]
= {x ϵ R : (x- 1)(x - 2)(x - 3) = 0}
= {x ϵ R: x = 1, 2, 3}
= {1, 2, 3}
Hence the set A, C and D are equal.
Sets – Exercise 1.3 – Q.4
A = {a, e, p, r}
B = {a, e, p, r} (repetition of 'p' is not allowed)
C = {e, o, p, r}
as A = B ≠ C, ∴ the sets are not equal
Sets – Exercise 1.3 – Q.5
Two finite sets are said to be equivalent if they have the same number of elements. As A and C have same number of elements, and B and D also have same number of elements.
∴ A is equivalent to C & 8 is equivalent to D.
Sets – Exercise 1.3 – Q.6
(i)
Two sets A and B are said to be equal if every elements of A is an elements of B and vice-versa.
We have, A = {2, 3} and
B = {x : x is a solution of x2 + 5x + 6 = 0
= {x : x2 + 3x + 2x + 6 = 0}
= {x : x (x + 3) +2(x +3 = 0)
= {x: (x + 3)(x +2) = 0}
= {x : x = -2, -3}
= (-2,-3)
Hence A ≠ B.
(ii)
A = {W, O, L, F}
B = {F, O, L, W} [∵ repetition is not allowed]
= {W, O, L F} [The order in which the elements are written does not matter.]
Hence A = B
Sets – Exercise 1.3 – Q.7
A = {0, a}
B = {1, 2, 3, 4}
C = {4, 8, 12}
D = {3, 1, 2, 4}
= {1, 2, 3, 4}
E = {1, 0}
F = {8, 4,12}
= {4, 8, 12}
G = {1, 5, 7, 11}
H = {a, b}
The sets B and D are equal.
The sets C and F are equal.
As A, E and H have same number of elements so they are equivalent.
As B, D and G have same number of elements, so they are equivalent
Also C and F have same number of elements, so they are equivalent.
Sets – Exercise 1.3 – Q.8
A = {1, 2}
B = {1, 2}
C = {3, 1}
D = {1, 3} [∵ the odd natural numbers less than 5 are 1 and 3]
E = {1, 2} [∵repetition is not allowed]
F = {1, 3} [∵repetition is not allowed]
∴ A, B and E are equal
Aslo, C, D and F are equal
Sets – Exercise 1.3 – Q.9
The set formed by distinct letters of the word "CATARACT' are (C, A, T ,R).
The set formed by distinct letters of the word "TRACT" are (T, R, A, C}
Hence the two set are equal.