10th Maths Sets Exercise 2.3 Solutions

Exercise 2.3 Solutions – Class X Mathematics

Exercise 2.3 Solutions – Class X Mathematics

These solutions are based on the Telangana State Class X Mathematics textbook, focusing on set equality and operations. Mathematical expressions are rendered using MathJax.

1. 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}

A = {F, O, L, W} (unique letters in “FOLLOW”).
B = {F, O, L, W} (unique letters in “FLOW”).
C = {W, O, L, F} (unique letters in “WOLF”).
Since A, B, and C contain the same elements {F, O, L, W}, they are equal.

Equal sets: A = B = C

2. 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 of vowels in English Alphabet}

(i) A … B: A = {1, 2, 3}, B = {1, 2, 3}, so A = B.
(ii) A … E: A = {1, 2, 3}, E = {a, e, i, o, u}, so A ≠ E.
(iii) C … D: C = {a, b, c, d}, D = {d, c, a, b}, so C = D.
(iv) D … F: D = {d, c, a, b}, F = {a, e, i, o, u}, so D ≠ F.
(v) F … A: F = {a, e, i, o, u}, A = {1, 2, 3}, so F ≠ A.
(vi) D … E: D = {d, c, a, b}, E = {a, e, i, o, u}, so D ≠ E.
(vii) F … B: F = {a, e, i, o, u}, B = {1, 2, 3}, so F ≠ B.

(i) A … B = =, (ii) A … E = ≠, (iii) C … D = =, (iv) D … F = ≠, (v) F … A = ≠, (vi) D … E = ≠, (vii) F … B = ≠

3. In each of the following, state whether A = B or not.

(i) A = {a, b, c, d}, B = {d, c, a, b}

A = {a, b, c, d}, B = {d, c, a, b}, same elements regardless of order.

Conclusion: A = B

(ii) A = {4, 8, 12, 16}, B = {8, 4, 16, 18}

A = {4, 8, 12, 16}, B = {8, 4, 16, 18}, B has 18 while A has 12.

Conclusion: A ≠ B

(iii) A = {2, 4, 6, 8, 10}, B = {x : x is a positive even integer and x < 10}

A = {2, 4, 6, 8, 10}, B = {2, 4, 6, 8} (x < 10).

Conclusion: A ≠ B

(iv) A = {x : x is a multiple of 10}, B = {10, 15, 20, 25, 30, …}

A = {10, 20, 30, …}, B includes 15, 25 (not multiples of 10).

Conclusion: A ≠ B

4. State the reasons for the following:

(i) {1, 2, 3, …, 10} ≠ {x : x ∈ ℕ and 1 < x < 10}

{1, 2, 3, …, 10} includes 1 and 10, while {x : x ∈ ℕ and 1 < x < 10} excludes 1 and 10.

Reason: Different element sets

(ii) {2, 4, 6, 8, 10} ≠ {x : x = 2n+1 and x ∈ ℕ}

{2, 4, 6, 8, 10} are even numbers, while {x : x = 2n+1 and x ∈ ℕ} are odd numbers (e.g., 1, 3, 5).

Reason: Different properties (even vs. odd)

(iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15}

{5, 15, 30, 45} includes 5 (not a multiple of 15), while {x : x is a multiple of 15} is {15, 30, 45, …}.

Reason: 5 is not a multiple of 15

(iv) {2, 3, 5, 7, 9} ≠ {x : x is a prime number}

{2, 3, 5, 7, 9} includes 9 (not prime), while {x : x is a prime number} is {2, 3, 5, 7, …}.

Reason: 9 is not a prime number

5. List all the subsets of the following sets.

(i) B = {p, q}

Subsets: {}, {p}, {q}, {p, q}.

Subsets: {}, {p}, {q}, {p, q}

(ii) C = {x, y, z}

Subsets: {}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}.

Subsets: {}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}

(iii) D = {a, b, c, d}

Subsets: {}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d}.

Subsets: {}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d}

(iv) E = {1, 4, 9, 16}

Subsets: {}, {1}, {4}, {9}, {16}, {1, 4}, {1, 9}, {1, 16}, {4, 9}, {4, 16}, {9, 16}, {1, 4, 9}, {1, 4, 16}, {1, 9, 16}, {4, 9, 16}, {1, 4, 9, 16}.

Subsets: {}, {1}, {4}, {9}, {16}, {1, 4}, {1, 9}, {1, 16}, {4, 9}, {4, 16}, {9, 16}, {1, 4, 9}, {1, 4, 16}, {1, 9, 16}, {4, 9, 16}, {1, 4, 9, 16}

(v) F = {10, 100, 1000}

Subsets: {}, {10}, {100}, {1000}, {10, 100}, {10, 1000}, {100, 1000}, {10, 100, 1000}.

Subsets: {}, {10}, {100}, {1000}, {10, 100}, {10, 1000}, {100, 1000}, {10, 100, 1000}

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