Question

Assume A is the set of positive integers less than 10 and B is the set of positive integers less than or equal to 20, and R is a relation from A to B defined as follows: R = {(a, b) | a ∈ A, b ∈ B, a is divisible by 4 ∧ b = 2a}. Which of the following ordered pairs belongs to that relation? Question 24 options: (6, 12) (16, 32) (12, 6) (8, 16) Question 25 (4 points) Given the relation R = {(n, m) | n, m ∈ ℤ, n ≥ m}. Which of the following statements about R is correct? Question 25 options: R is not a partial order because it is not antisymmetric R is not a partial order because it is not reflexive R is a partial order R is not a partial order because it is not transitive

Answer 1

The set of elements of the given relation

R = {(a, b) | a ∈ A, b ∈ B, a is divisible by 4 and b = 2a} is

R = { (4 , 8) , (8 , 16)}

Given, A is the set of positive integers less than 10

and B is the set of positive integers less than or equal to 20,

and R is a relation from A to B defined as follows:

R = {(a, b) | a ∈ A, b ∈ B, a is divisible by 4 and b = 2a}.

we have to find the ordered pairs which belong to the given relation,

As, 'a' should be divisible by 4 and we should also get 'b' by multiplying 'a' by 2.

So, the set of elements of the relation R is,

R = { (4 , 8) , (8 , 16)}

Hence, the set of elements of the given relation

R = {(a, b) | a ∈ A, b ∈ B, a is divisible by 4 and b = 2a} is

R = { (4 , 8) , (8 , 16)}

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