Telangana SCERT Class 10 Maths Chapter 2 Sets Exercise 2.3 Maths Problems and Solution Here in this Post. Telangana SCERT Class 10 Maths Solution Chapter 2 Sets Exercise 2.3
Telangana SCERT Solution Class X (10) Maths Chapter 2 Sets Exercise 2.3
Exercise – 2.3
(Q1) Which of the following sets are equal?
A = {x : x is a letter in the word FOLLOW},
B = {x : x is a letter in the word FLOW}
And C = {x : x is a letter in the word WOLF}
=> Solution:
First we have to convert set-builder form into roaster form.
The roaster form of the given sets are.
A = {F, O, L, W} = {f, o, l, w}
B = {F, L, O, W} = {f, l, o, w}
C = {W, O, L, F} = {w, o, l, f}
∴in all the sets of elements are equal.
∴ A = B = C
∴ All the three sets are equal.
(Q2) Consider the following sets and fill up the blanks with = or ≠
So as to make the statement true A = {1, 2, 3}; B = {The first three natural numbers}
C = {a, b, c, d}; D = {d, c, a, b}
E = {a, e, I, o, u};
F = {set or vowels in English alphabet}
(i) First we have to convert set – builder form in to roaster form of set B and F.
The roaster form of set B & F is
B = {1, 2, 3}
F = {a, e, i, o, u}
A = {1, 2, 3}
C = {a, b, c, d}
D = {d, c, a, b}
E = {a, e, I, o, u}
(i) A —— B
=> A = {1, 2, 3} and B = {1, 2, 3}
∴ A = B
[∴The set A and B are of equal elements]
(ii) A —– E
=> A = {1, 2, 3} and E = {a, e, I, o, u}
∴ A ≠ E
[The set A and E are different sets]
(iii) C —- D
=> C = {a, b, c, d} and D = {d, c, a, b}
∴ C = D
[The set C and D are of equal elements]
(iv) D —- F
=> D = {d, c, a, b} and F = {a, e, i, o, u}
D ≠ F
[The set D and F are different sets of elements]
(v) F —– A
=> F = {a, e, i, o, u} and A = {1, 2, 3}
F ≠ A
[The set F and A are different sets of elements]
(vi) D — E
= D = {d, c, a, b} and E = {a, e, i, o, u}
∴ D ≠ E
[The sets D and E are different sets of element]
(vii) F —- B
= F = {a, e, i, o, u} and B = {1, 2, 3}
∴ F ≠ B
[The set F and B are different sets of elements]
(Q3) In each of the following, state whether A = B or not
(i) A = {a, b, c, d} B = {d, c, a, b}
=> A = B
[The set A and B are equal elements]
(ii) A = {4, 8, 12, 16} B = {8, 4, 16, 18}
= A ≠ B
[The set A and B are different sets of elements]
(iii) A = {2, 4, 6, 8, 10} B = {x : x is a positive even integer and x <10}
=> First we have convert set-builder form into roaster form.
A = {2, 4, 6, 8, 10} B = {2, 4, 6, 8}
A ≠ B
[The set A and B are different sets of elements]
(iv) A = {x : x is multiple of 10}
B = {10, 15, 20, 25, 30, —-}
=> First we have to convert set builder form into roaster form
A = {10, 20, 30, —}
B = {10, 15, 20, 25, 30, —-}
A ≠ B
The set A and B are different sets of elements]
(Q4) State the reason for the following
(i) {1, 2, 3, — 10} ≠ {x : x ∈ N and 1< x <10}
= First we have convert set builder form into roaster form
{x : x∈N and 1< x <10}
{1, 2, 3, —- 10} ≠ {2, 3, 4, 5, 6, 7, 8, 9}
We see that both the sets are different sets of elements.
Hence, these sets are not equal sets.
(ii) {2, 4, 6, 8, 10} ≠ {x : x = 2∩+1 and x∈N}
= First we have to convert set-builder form into roaster form.
{2, 4, 6, 8, 10} ≠ {3, 5, 7, 9, —}
[N = 1, 2(1) +1 = 3, 2(2) +1 = 5, 2(3) +1 =7 —]
We see that both the sets are different sets of elements.
Hence, these sets are not equal sets.
(iii) {5, 15, 30, 45} ≠ {x : x is multiple of 15}
=> First we have to convert set – builder form in to roaster form.
{5, 15, 30, 45} ≠ {15, 30, 45, 60, —-}
We see that both the sets are different sets of elements.
Hence, these sets are not equal sets
(iv) {2, 3, 5, 7, 9} ≠ {x : x is a prime number}
=> First we have to convert set-builder form into roaster form.
{2, 3, 7, 5, 9} ≠ {2, 3, 5, 7, 11 —-}
Again both the sets are different sets of elements.
Hence, these sets are not equal sets
(Q5) List all the subsets of the following sets
B = {P, q}
=> Total number of subsets = 2∩
Where ∩ = number of elements]
Here, ∩ = 2
Number of subsets = 22 = 4
List of all subsets of set B are,
(i) Null is a se subset of every set so,
∅
(ii) {p}
(iii) {q)
(iv) B
(ii) C = {x, y, z)
Here, ∩ = 3
By using formula of subset
Total number of = 2∩ subsets
∴ Total number of = 23 subsets
∴ Total number of = 8 subsets
∴ List of all subsets of set C are.
(i) ∅
(ii) {x}
(iii) {y}
(iv) {z}
(v) {xy}
(vi) {yz}
(vii) {xz}
(viii) C
[∵Every set is a subset of itself]
(iii) D = {a, b, c, d}
=> By using formula of subset
∴ Total number of = 2∩ Subsets
here, ∩ = 4
= 24
Total number of = 16 subsets
List of all subsets of set D are
(i) ∅
(ii) {a}
(iii) {b}
(iv) {c}
(v) {d}
(vi) {a, b}
(vii) {b, c}
(viii) {c, d}
(ix) {a, b}
(x) {b, d}
(xi) {c, d}
(xii) {a, b, c}
(xiii) {a, c, d}
(xiv) {a, b, d}
(xv) {b, c, d}
(xvi) D
(iv) E = {1, 4, 9, 16}
=> By using formula of subset
Total number of = 2∩ subsets
∴ Here, ∩ = 4
∴ Total number of 24 subsets
= 16
List of all subsets of set E are.
(i) ∅
(ii) {1}
(iii) {4}
(iv) {9}
(v) {16}
(vi) {1,4}
(vii) {1,9}
(viii) {1,16}
(ix) {9,16}
(x) {1,4,9}
(xi) {1,4,16}
(xii) {1,9,16}
(xiii) {4,9,16}
(xiv) {4,9}
(xv) {4,16}
(xvi) E
(v) F = {10, 100, 1000}
=> By using formula of subset
Total number of = 2∩ subsets
Here, ∩ = 3
∴ Total number of = 23 subsets
= 8
List of all subsets of set E are.
(i) ∅
(ii) {10}
(iii) {100}
(iv) {1000}
(v) {10,100}
(vi) {100,1000}
(vii) {10,1000}
(viii) F