The relation R = a , b : g c d a , b = 1 , 2 a ≠ b , a , b ∈ ℤ is:

Step-by-step solution

Given relation is R = a , b : g c d a , b = 1 ,   2 a ≠ b ,   a ,   b ∈ ℤ Now, Reflexive: gcd a , a ≠ 1   ∀ a ∈ Z , hence R is not reflexive. Symmetric: a = 2 ,   b = 1 ⇒ gcd 2 , 1 = 1 Also, 2 a = 4 ≠ b Now when a = 1 ,   b = 2 ⇒ g c d ( 1 ,   2 ) = 1 But, 2 a = 2 = b Hence, a = 2 b ⇒ R is not Symmetric Transitive: Let a = 14 ,   b = 19 ,   c = 21 g c d ( a ,   b ) = 1 g c d ( b ,   c ) = 1 g c d ( a ,