Mathematics
For each of the following pairs of sets, identify the disjoint and overlapping sets :
(i)
A = {x : x is a prime number, x < 8}.
B = {x : x is an even natural number, x < 8}.
(ii) C = {x : x ∈ N, x < 10} and D = {x : x ∈ N, x is a multiple of 5}.
(iii) E = {x : x = 4n, n ∈ N} and F = {x : x = 9n, n ∈ N}.
(iv) G = {x : x = 8n, n ∈ N and n < 7} and H = {x : x = 9n, n ∈ N and n < 7}.
Related Questions
Identify the null sets among the following :
(i) A = {x : x is a whole number, x < 1}.
(ii) B = {x : x is a number, x > x}.
(iii) C = {x : x is an even prime number}.
(iv) D = {x : x ∈ I, x2 = -4}.
(v) E = {x : x is a perfect square number, 40 < x < 50}.
(vi) F = {x : x ∈ N, 5 < x < 6}.
Identify whether the given pair consists of equal or equivalent but not equal sets or none :
(i) A = set of letters of the word 'FLOWER'.
B = set of letters of the word 'FOLLOWER'.(ii) C = {x : x ∈ N, x + 5 = 6} and D = {x : x ∈ W, x < 1}.
(iii) E = set of first five whole numbers.
F = set of first five natural numbers.(iv) G = {a, b, c} and H = {x, y, z}.
(v) J = {x : x ∈ N, x ≠ x} and K = {x : x ∈ N, 6 < x < 7}.
State in each case, whether the given statement is true or false :
(i) If A is the set of all non-negative integers, then 0 ∈ A.
(ii) If B is the set of all consonants, then c ∈ B.
(iii) If C is the set of all prime numbers less than 80, then 57 ∈ C.
(iv) {x : x ∈ W, x + 5 = 5} is a singleton set.
(v) If D = {x : x ∈ W, x < 4}, then n(D) = 4.
(vi) {a, b, c, 1, 2, 3} is not a set.
(vii) {1, 2, 3, 1, 2, 3, 1, 2, 3,……………} is an infinite set.
(viii) 0 ∈ Φ.
(ix) {3, 5} ∈ (1, 3, 5, 7, 9).
Indicate whether the given statement is true or false :
(i) {Triangles} ⊆ {Quadrilaterals}
(ii) {Squares} ⊆ {Rectangles}
(iii) {Rhombuses} ⊆ {Parallelograms}
(iv) {Natural numbers} ⊆ {Whole numbers}
(v) {Integers} ⊆ {Whole numbers}
(vi) {Composite numbers} ⊆ {Odd numbers}