Which of the following are examples of empty set? (i) Set of all even natural numbers divisible by 5. (ii) Set of all even prime numbers. (iii) {x: x^2 – 2 = 0 and x is rational }. (iv) {x: x is a natural number, x less than 8 and simultaneously x greater than 12}. (v) {x: x is a point common to any two parallel lines }. Watch Solution
Which of the following sets are finite and which are infinite? (i) Set of concentric circles in a plane. (ii) Set of letters of the English Alphabets. (iii) (x ∈N : x > 5} (iv) {x ∈N : x < 200} (v) {x ∈Z : x < 5} (vi) {x ∈R : 0 < x < 1}. Watch Solution
Which of the following sets are equal? (i) A = {1, 2, 3} (ii) B= {x∈R : x^2 -2x +1 = 0} (iii) C = {1, 2, 2, 3} (iv) D= {x∈R : x^3 – 6x^2 + 11x – 6 = 0}. Watch Solution
Are the following sets equal? A = {x : x is a letter in the word reap}, B = {x: x is a letter in the word paper), C = {x : x is a letter in the word rope} Watch Solution
From the set given below, pair the equivalent sets A = {1, 2, 3}, B = {t, p ,q, r, s}, C = {α, β, γ}, D = {a, e, i, o, u}. Watch Solution
Are the following pairs of sets equal? Give reasons. (i) A = {2, 3}, B = {x: x is a solution of x^2 + 5x + 6 = 0} (ii) A = {x:x is a letter of the word “WOLF”}, B = {x: x is a letter of the word “FOLLOW”} Watch Solution
From the sets given below, select equal sets and equivalent sets. A = {0, a}, B = {1, 2, 3, 4}, C = {4, 8, 12}, D = {3, 1, 2, 4}, E = {1, 0}, F = {8, 4, 12}, G = {1,5,7,11}, H = {a, b} Watch Solution
Which of the following sets are equal? A = {x: x∈ N, x < 3), B = {1,2},C = {3,1}, D= {x: x∈ N, x is odd, x < 5}, E = {1,2,1,1}, F = {1,1, 3}. Watch Solution
Show that the set of letter needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal. Watch Solution