What is Reflexive Relation?(chapter-relation and function). plz don't post irrlevent answers..
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Can you give an example of a relation that is symmetric and transitive, but not reflexive?
By definition,
RR, a relation in a set X, is reflexive if and only if ∀x∈X∀xX, xRxxRx.
RR is symmetric if and only if ∀x,y∈X∀xyX, xRy⟹yRxxRyyRx.
RR is transitive if and only if ∀x,y,z∈X∀xyzX, xRy∧yRz⟹xRzxRyyRzxRz.
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.
By definition,
RR, a relation in a set X, is reflexive if and only if ∀x∈X∀xX, xRxxRx.
RR is symmetric if and only if ∀x,y∈X∀xyX, xRy⟹yRxxRyyRx.
RR is transitive if and only if ∀x,y,z∈X∀xyzX, xRy∧yRz⟹xRzxRyyRzxRz.
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.
PIB:
thanks fr d answer
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