Q. 85.0( 1 Vote )

# Mark the tick against the correct answer in the following:Let Z be the set of all integers and let R be a relation on Z defined by a R b ⇔ a≥ b. Then, R isA. symmetric and transitive but not reflexiveB. reflexive and symmetric but not transitiveC. reflexive and transitive but not symmetricD. an equivalence relation

According to the question ,

Given set Z = {1, 2, 3 ,4 …..}

And R = {(a, b) : a,b Z and a ≥ b}

Formula

For a relation R in set A

Reflexive

The relation is reflexive if (a , a) R for every a A

Symmetric

The relation is Symmetric if (a , b) R , then (b , a) R

Transitive

Relation is Transitive if (a , b) R & (b , c) R , then (a , c) R

Equivalence

If the relation is reflexive , symmetric and transitive , it is an equivalence relation.

Check for reflexive

Consider , (a,a) (b,b)

a a and b b which is always true.

Therefore , R is reflexive ……. (1)

Check for symmetric

a R b a b

b R a b a

Both cannot be true.

Ex _ If a=2 and b=1

2 1 is true but 1 2 which is false.

Therefore , R is not symmetric ……. (2)

Check for transitive

a R b a b

b R c b c

a c

Ex _a=5 , b=4 and c=2

5≥4 , 4≥2 and hence 5≥2

Therefore , R is transitive ……. (3)

Now , according to the equations (1) , (2) , (3)

Correct option will be (C)

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