Solution: (4) f (x) = x2 + bx + c It is a quadratic equation. The value of a is positive. The minimum value is (-b / 2a, -D / 4a). It is... View Article
Solution: (5) Given: A ={1, 3, 5, 7}; B = {1, 2, 3, 4, 5, 6, 7, 8} n (A) = 4 and n (B) = 8 The number of one-one function from A into B is... View Article
Solution: (1) aRB => a = 2k .b, k ∈ I Reflexive: (a, a) ∈ R k = 0, a = 20 b = b aRa Symmetric: If a = 2k .b then b = 2-kb where k, -k... View Article
Solution: (3) (a, a) ∈ R R is reflexive. (a, b) ∈ R ⇒ a lives within one kilometre from b ⇒b lives within one kilometre from a So, (a, b)... View Article
Solution: (1) The given relation is R = {(x, y) ∈ W × W : the words x and y have at least one letter in common} Reflexive: (a, a) ∈ R If a... View Article
Solution: (2) Given: a differs from b by 3 a - 3 = b a = b + 3 If N = 1, 2, 3, 4… b = 1, a = 4 b = 2, a = 5 b = 3, a = 6 The relation... View Article
Solution: (2) aRb ⇒ GCD of a and b is 2 Reflexive: (a, a) ∈ R aRa ⇒ GCD (a, a) = a (3, 3) ∉ R (4, 4) ∉ R Symmetric (a, b) ∈ R ⇒ GCD (a,... View Article
Solution: (1) If x is a real number, x − x = 0 ∈ set of integers I (x, x) ∈ T It is reflexive. (x, y) ∈ T; (y, x) ∈ T x − y = I; y − x ∈ I... View Article
Solution: (1) x2 - 4xy + 3y2 = 0 (x - y) (x - 3y) = 0 (a, a) ∈ R (a - a) (a - 3a) = 0 Relation is reflexive (a, b) ∈ R (b, a) ∈ R (3,... View Article
Solution: (1) a ∈ R a - a + √3 = √3 is an irrational number (a, a) ∈ R R is reflexive. a, b ∈ R a - b + √3 is an irrational number b - a... View Article
Solution: (2) Consider A = {a, b, c} R: A → A S: A → A If R and S are reflexive, R ⋃ S is reflexive. R ⋂ S is reflexive If R & S are... View Article
