Give an example of a binary relation which is connected and transitive but not reflexive
Answers
Answered by
0
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.
Similar questions
Geography,
6 months ago
English,
6 months ago
English,
6 months ago
Math,
1 year ago
Accountancy,
1 year ago