Question

Determine whether the relation Ron Q - {0} defined by (a,b) ER
ab=4 is reflexive , symmetric and transitive ​

Answer 1

Given: Relation R on Q - {0} defined by (a,b)∈R  ab=4

To find: Determine whether the relation is reflexive , symmetric and transitive ​.

Solution:

• Now we have given the relation:

                 R = { (a,b) ∈ R => ab = 4 }

• The possible order might be:

                 R = { (1,4) , (2,2) , (4,1) }

• For reflexive, we have:

                 (a,a) ∈ R

                 Here (1,1) and (4,4) ∉ R, so R is not reflexive.

• For symmetric, we have:

                 (a,b) ∈ R and (b,a) ∈ R

                 Here (1,4) and (4,1) ∈ R, so R is symmetric.

• For transitive, we have:

                 (a,b) ∈ R and (b,c) ∈ R then (a,c) ∈ R

                 Here (1,4) and (4,1) ∈ R, but (1,1) ∉ R so R is not transitive.

Answer:

              So the relation is symmetric.