If a relation is symmetric and transitive on any non-empty set, then it is reflexive. Is it true or false? State with reason.

Given an example of a relation which is symmetric, transitive but not reflexive.

Let R be a relation on X, If R is symmetric then xRy impliesyRx . If it is also transitive then xRy and yRx implies xRx .So whenver a relation is symmetric and transitive then it is also reflexive. What is wrong in this argument ?

state true or false k[0]=0,k inR

If A is a symmetric matrix, then A- A is both symmetric and skew symmetrix. State true or false.

Give an example of a relation, which is (i) symmetric but neither reflexive nor transitive. (ii) transitive but neither reflexive nor symmetric. (iii) reflexive and symmetric but not transitive. (iv) reflexive and transitive but not symmetric. (v) symmetric and transitive but not reflexive.

Given an example of a relation which is reflexive, transitive but not symmetric.

Given an example of a relation which is reflexive but neither symmetric nor transitive.

Give an example of a relation which is reflexive, transitive but not symmetric.

Test whether the relations are reflexive, symmetric or transitive on the sets specified. R=(m,n}: mn is divisible by 2) on Z.