Question

Give an example of a binary relation which is connected and transitive but not reflexive

Answer 1

Step-by-step explanation:

RR, a relation in a set XX, is reflexive if and only if ∀x∈X∀x∈X, xRxxRx.

RR is symmetric if and only if ∀x,y∈X∀x,y∈X, xRy⟹yRxxRy⟹yRx.

RR is transitive if and only if ∀x,y,z∈X∀x,y,z∈X, xRy∧yRz⟹xRzxRy∧yRz⟹xRz.

I can give a relation ⩽⩽, in a set of real numbers, as an example of reflexive and transitive, but not symmetric. But I can't think of a relation that is symmetric and transitive, but not reflexive.