Question

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is reflexive

Answer 1

N = the set of natural numbers.

R is the relation defined on N by

a R b if a + b ≤ 6

R = {(a, b), a, b ∈ N / a + b ≤ 6}

a + b ≤ 6 ⇒ b ≤ 6 – a

a = 1,

b ≤ 6 – 1 = 5

b is 1, 2, 3, 4, 5

∴ (1, 1), (1, 2), (1, 3), (1, 4), (1, 5) ∈ R

a = 2,

b ≤ 6 – 2 = 4

b is 1, 2, 3, 4

∴ (2, 1), (2, 2), (2, 3), (2, 4) ∈ R

a = 3,

b < 6 – 3 = 3

b is 1, 2, 3

∴ (3, 1), (3, 2), (3, 3) ∈ R

a = 4 ,

b < 6 – 4 = 2

b is 1, 2

∴ (4, 1), (4, 2) ∈ R

a = 5,

b < 6 – 5 = 1

b is 1

∴ (5, 1) ∈ R

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

Reflexive:

R is not reflexive since (4, 4), (5, 5) ∈