Q: Determine whether the relation is reflexive, symmetric and transiti

1.	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» EXPLANATION. R is set of N NATURAL number defined as, ⇒ R = {(x, y) : y = x + 5 and x < 4}. As we know that, x and y ∈ N. ⇒ x < 4. Values of x = {1, 2, 3}. ⇒ y = x + 5. Put the value of x = 1 in the equation, we get. ⇒ y = 1 + 5. ⇒ y = 6. Put the value of x = 2 in the equation, we get. ⇒ y = 2 + 5. ⇒ y = 7. Put the value of x = 3 in the equation, we get. ⇒ y = 3 + 5. ⇒ y = 8. ⇒ R = {(1,6), (2,7), (3,8)}. For reflexive. ⇒ x ∈ (a, a) for every a ∈ N. ⇒ (1,1), (2,2), (3,3) ∉ R. So, it is not a reflexive. For transitive. If (a, B) ∈ R then (b, C) ∈ R and (a, c) ∈ R. In this equation no one pair is matched. So, it is not a transitive. For symmetric. If (a, b) ∈ R then (b, a) ∈ R. In this equation no one pair is like this. So, it is not a symmetric.

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»

R is set of N NATURAL number defined as,

⇒ R = {(x, y) : y = x + 5 and x < 4}.

As we know that,

x and y ∈ N.

⇒ x < 4.

Values of x = {1, 2, 3}.

⇒ y = x + 5.

Put the value of x = 1 in the equation, we get.

⇒ y = 1 + 5.

⇒ y = 6.

Put the value of x = 2 in the equation, we get.

⇒ y = 2 + 5.

⇒ y = 7.

Put the value of x = 3 in the equation, we get.

⇒ y = 3 + 5.

⇒ y = 8.

⇒ R = {(1,6), (2,7), (3,8)}.

For reflexive.

⇒ x ∈ (a, a) for every a ∈ N.

⇒ (1,1), (2,2), (3,3) ∉ R.

So, it is not a reflexive.

For transitive.

If (a, B) ∈ R then (b, C) ∈ R and (a, c) ∈ R.

In this equation no one pair is matched.

So, it is not a transitive.

For symmetric.

If (a, b) ∈ R then (b, a) ∈ R.

In this equation no one pair is like this.

So, it is not a symmetric.