Let A = {1, 2, 3, 4, 5, 6} and let R = {(a, b): a, b ∈ A and b = a +

1.	Let A = {1, 2, 3, 4, 5, 6} and let R = {(a, b): a, b ∈ A and b = a + 1}.Show that R is (i) not reflexive, (ii) not symmetric and (iii) not transitive.
Answer» By using roster form R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} (i) Non reflexive We know that (1, 1) ∈ R where 1 ∈ A Hence, R is non reflexive. (ii) Non symmetric We know that (1, 2) ∈ R but (2, 1) ∉ R Hence, R is non symmetric. (iii) Non transitive We know that (1, 2) ∈ R and (2, 3) ∈ R In the same way (1, 3) ∉ R Hence, R is non transitive.

Let A = {1, 2, 3, 4, 5, 6} and let R = {(a, b): a, b ∈ A and b = a + 1}.Show that R is (i) not reflexive, (ii) not symmetric and (iii) not transitive.

Answer»

By using roster form

R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

(i) Non reflexive

We know that

(1, 1) ∈ R where 1 ∈ A

Hence, R is non reflexive.

(ii) Non symmetric

We know that

(1, 2) ∈ R but (2, 1) ∉ R

Hence, R is non symmetric.

(iii) Non transitive

We know that

(1, 2) ∈ R and (2, 3) ∈ R

In the same way (1, 3) ∉ R

Hence, R is non transitive.

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Let A = {1, 2, 3, 4, 5, 6} and let R = {(a, b): a, b ∈ A and b = a + 1}.Show that R is (i) not reflexive, (ii) not symmetric and (iii) not transitive.

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