Which of the following statements are true? Give reason to support your answer. (i) For any two sets A and B either A ⊆ B or B ⊆ A. (ii) Every subset of an infinite set is infinite. (iii) Every subset of a finite set is finite. (iv) Every set has a proper subset. (v) {a, b, a, b, a, b, …} is an infinite set. (vi) {a, b, c} and {1, 2, 3} are equivalent sets. (vii) A set can have infinitely many subsets. Watch Solution
State whether the following statements are true or false: (i) 1 ∈ {1, 2, 3} (ii) a ⊂ {b, c, a} (iii) (a) ∈ (a, b, c} (iv) {a, b} = {a, a, b, b, a} (v) The set {x: x + 8 = 8} is the null set. Watch Solution
Decide among the following sets, which are subsets of which: A = {x:x satisfies x^2 – 8x + 12 = 0}, B = {2, 4, 6}, C = {2, 4, 6, 8,….}, D = {6}. Watch Solution
Write which of the following statements are true? Justify your answer. (i) The set of all integers is contained in the set of all rational numbers. (ii) The set of all crows is contained in the set of all birds. (iii) The set of all rectangles is contained in the set of all squares. (iv) The set of all real numbers is contained in the set of all complex numbers. (v) The sets P = {a} and B = {{a}} are equal. (vi) The sets A = {x: x is a letter of the word “LITTLE”} and, B = {x: x is a letter of the word “TITLE” } are equal. Watch Solution
Which of the following statements are correct? Write a correct form of each of the incorrect statements. (i) a ⊂ {a, b, c} (ii) {a} ∈ {a, b, c} (iii) a ∈ {{a}, b} (iv) {a} ⊂ {{a}, b} (v) {b, c} ⊂ {a, (b, c)} (vi) {a, b} ⊂ {a, (b, c}} (vii) Φ ∈ {a, b} (viii) Φ ⊂ {a, b, c} (ix) {x: x + 3 – 3} = Φ Watch Solution
Let A = {a, b, {c, d), e}. Which of the following statements are false and why? (i) {c, d} ⊂ A (ii) {c, d} ∈ A (iii) {{c, d}} ⊂ A (iv) a ∈ A (v) a ⊂ A (vi) {a, b, e} ⊂ A (vii) {a, b, e} ∈ A (viii) {a, b, c} ⊂ A (ix) Φ ∈ A (x) {0} ⊂ A Watch Solution
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: (i) 1 ∈ A (ii) {1, 2, 3} ⊂ A (iii) {6,7,8} ∈ A (iv) {{4, 5}} ⊂ A (v) ф ∈ А (vi) ф ⊂ А Watch Solution
Let A = {0, {ф}, 1, {1, ф}), 2}. Which of the following are true?M (i) ф ∈ А (ii) {ф} ∈ A (iii) {1} ∈ A (iv) {2, 0} ⊂ A (v) 2 ⊂ A (vi) (2, {1}} ⊄ A (vii) {{2},{1}} ⊄ A (viii) {0, {0}, {1, 0}} ⊂ A (ix) {{0}} ⊂ A. Watch Solution
Write down all possible subsets of each of the following sets: (i) {a} (ii) {0, 1} (iii) {a, b, c } (iv) {1, {1}} (v) {ф} Watch Solution
Write down all possible proper subsets each of the following sets: (i) {1,2} (ii) {1, 2, 3} (iii) {1} Watch Solution
What is the total number of proper subsets of a consisting of n elements ? Watch Solution
If A is any set, prove that : A ⊆ ф ⟺ A = ф. Watch Solution
Prove that : A ⊆ B, B ⊆ C and C ⊆ A ⟺ A = C. Watch Solution
What universal set (s) would you propose for each of the following : (i) The set of right triangles. (ii) The set of isosceles triangles. Watch Solution
If X = {8^n – 7n – 1: n ∈ N} and Y = {49(n – 1) : n ∈ N}, then prove that X ⊆ Y. Watch Solution