Question

Q: Determine whether the relation is reflexive, symmetric and transitive:
Relation R is the set N of natural numbers defined as,
ㅤㅤㅤ R = {(x, y) : y = x + 5 and x < 4}​

Answer 1

Answer:

R={(x,y):y=x+5andx<4}={(1,6),(2,7),(3,8)}

It is seen that (1,1)∈

/

R⇒R is not reflexive.

Also (1,6)∈R.

But, (1,6)∈

/

R. ∴R is not symmetric.

Now, since there is no pair in R such that (x,y) and (y,z)∈R, then (x,z) cannot belong to R.

∴R is transitive.

Hence, R is neither reflexive, nor symmetric, but transitive

Answer 2

Answer:

A = {1, 2, 3,………… }

R = {(1,6), (2,7), (3,8)}

because x < 4 R is not reflexive as (1,1) ∈ R

R is not symmetric as (2,7) ∈ R but (7,2) ∉ R

R is Transitive as transitivity is not contradicted.