Question

the relation "<"is *
1 point
O reflexive
O not reflextive
O symmetric
reflexive and symmetric
This is a required question​

Answer 1

Answer:

Can you give an example of a relation that is symmetric and transitive, but not reflexive?

By definition,

R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx.

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

R is transitive if and only if ∀x,y,z∈X, xRy∧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