Question

Find whether following relation are symmetric, reflexive and transitive

a) R is a relation on set of people, two people a,b are said to be in relation iff “a is the mother of b”

b) R is a relation on all the sets. Two sets A,B are said to be in relation iff “A is subset of B”

c) If R is a relation defined as aRb iff ->0ab​

Answer 1

Answer:

Relation 1 is

not reflexive.

not symmetric.

not transitive.

Relation 2 is

reflexive.

not symmetric.

transitive.

Relation 3 (aRb if ab > 0) is

reflexive.

symmetric.

transitive.

Step-by-step explanation:

1)

Since aRb if a is the mother of b.

Since a can not a mother of itself.

So the relation 1 is not reflexive.

if a mother of b then b is not the mother of a.

So the relation 1 is not symmetric.

If a is mother of b and b is mother of c then a is grand mother of c not the mother of c.

So the relation 1 is not transitive.

2)

Since A relation B if A subset of B.

Since A is subset of A itself.

So the relation 2 is reflexive.

Since if A is subset of B then it may be that B is subset of A or may be not.

So the relation 2 is not symmetric.

If A is subset of B and B is subset of C then A is subset of C.

So the relation 2 is transitive.

3)

a relation b if ab > 0

Since   a×a = a² > 0 so

Relation 3 is reflexive.

If ab > 0 then ba > 0

so Relation 3 is symmetric.

If ab > 0 and bc > 0 then ac > 0

so Relation 3 is transitive.