solution: R = {(a, b) : a = b – 2, b > 6} (A) Incorrect : Value of b = 4, false. (B) Incorrect : a = 3 and b = 8 > 6 a = b – 2 => 3 = 8 – 2 and 3 = 6, which is bogus. (C) Correct: a = 6 and b...

solution: Once more, The arrangement of all lines identified with the line y = 2x + 4, is the arrangement of all its equal lines. Incline of given line is m = 2. As we probably are aware slant of...

solution: Case I: R = {(P1, P2) :P1 and P2 have same number of sides} Check for reflexive: P1 and P1 have same number of sides, So R is reflexive. Check for symmetric: P1 and P2 have same number of...

solution: Case I: T1, T2 are triangle. R = {(T1, T2): T1 is like T2} Check for reflexive: As We realize that every triangle is like itself, so (T1, T1) ∈ R is reflexive. Check for symmetric:...

solution: R = {(P, Q): distance of the point P from the beginning is equivalent to the distance of the point Q from the origin} Say "O" is beginning Point. Since the distance of the point P from the...

solution: (I) A = {x ∈ Z : 0 ≤ x ≤ 12} In this way, A = {0, 1, 2, 3, … … , 12} Presently R = {(a, b) : |a – b| is a different of 4} R = {(4, 0), (0, 4), (5, 1), (1, 5), (6, 2), (2, 6), ….., (12, 9),...

Solution:A = {1, 2, 3, 4, 5} and R = {(a, b) : |a – b| is even} We get, R = {(1, 3), (1, 5), (3, 5), (2, 4)} For (a, a), |a – b| = |a – a| = 0 is even. Therfore, R is reflexive. If |a – b| is even,...

solution: Books x and x have same number of pages. (x, x) ∈ R. R is reflexive. In the event that (x, y) ∈ R and (y, x) ∈ R, so R is symmetric. Since, Books x and y have same number of pages and...

solution: R = {(1, 2), (2, 1)} (x, x) ∉ R. R isn't reflexive. (1, 2) ∈ R and (2,1) ∈ R. R is symmetric. Once more, (x, y) ∈ R and (y, z) ∈ R then, at that point (x, z) doesn't suggest to R. R isn't...

solution: R = {(a, b) : a ≤ b3} a ≤ a3: which is valid, (a, a) ∉ R, So R isn't reflexive. a ≤ b3 however b ≤ a3 (bogus): (a, b) ∈ R yet (b, a) ∉ R, So R isn't symmetric. Once more, a ≤ b3 and b ≤ c3...

Solution: a ≤ a: which is valid, (a, a) ∈ R, So R is reflexive. a ≤ b yet b ≤ a (bogus): (a, b) ∈ R however (b, a) ∉ R, So R isn't symmetric. Once more, a ≤ b and b ≤ c then a ≤ c : (a, b) ∈ R and...

solution: R = {(a, b) : b = a + 1} R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} At the point when b = a, a = a + 1: which is bogus, So R isn't reflexive. In the event that (a, b) = (b,a), b = a+1...

Solution: R = {(a, b) : a ≤ b2} , Relation R is characterized as the arrangement of genuine numbers. (a, a) ∈ R then a ≤ a2 , which is bogus. R isn't reflexive. (a, b)=(b, a) ∈ R then a ≤ b2 and b ≤...

Relation R in the set A of human beings in a town at a particular time given by R = {(x, y) : x and y work at the same place}R = {(x, y) : x and y live in the same locality}R = {(x, y) : x is...

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer} (iii) R = {(x, y) : y is...