Question

Letbe a relation defined by. The relationis (a) reflexive, symmetric and transitive (b) reflexive, transitive but not symmetric (c) symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric​

Answer 1

Answer:

a) RELATION BETWEEN REFLEXIVE SYMMETRIC AND TRANSITIVE ----------

A given binary relation -on a set x is said to be an equivalence relation if and only if it is reflexive symmetric and transitive.

b) Relation R = {( a, b )}:a <b is transitive and reflexive but not symmetric.

c) ➡ R , a relation in a set x, is reflexive if and only if x £x, x.

➡ 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.

d) Let A = { x, y, z }

define a reflexive R on A as R = { x, y } , {y, x }.

R is not reflexive as, (×, ×) , (y, y ) , (z, z ) £R .

Symmetric ---

= ( x , y ) ( y , x ) £ R ,

R is not transitive.