Question

show that the relation "less than or equal to" on the set of integers Z ,is reflexive and transitive but not symmetric​

Answer 1

TO FIND :

Show that the relation " ≤ "

on the set of integers Z ,is reflexive and transitive but not symmetric​.

SOLUTION:

◆Since x £ Z ,

x ≤ x , is possible

So, (x,x) £ Z - relation is reflexive .

◆Since( x,y) £ Z ,

y ≤ x

x ≤ y , is not possible ,

As (x,y) £ Z ,integers

◆For example ,

-2 ≤ 3 ,

3 ≤/ -2; 3 is never less than or equal to -2.

◆So, (x,y) £ Z - relation is not symmetric.

◆But, Since( x,y)(y,z) £ Z ,

x ≤ y ;y ≤ z

x ≤ z , is possible

So, (x,y)(y,z) £ Z - relation is transitive.

◆Thus the relation " ≤ "on the set of integers Z ,is reflexive and transitive but not symmetric​.