Question Video: Verifying Pairs of a Relation on a Set given Its Rule | Nagwa Question Video: Verifying Pairs of a Relation on a Set given Its Rule | Nagwa

# Question Video: Verifying Pairs of a Relation on a Set given Its Rule Mathematics • Third Year of Preparatory School

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If set 𝑋 = {6, 12, 18, 24, 27, 29, 36} and 𝑅 is a relation on 𝑋, where 𝑎 𝑅𝑏 signifies that 𝑎 is twice 𝑏. Given that 𝑎 ∈ 𝑋, 𝑏 ∈ 𝑋, and 𝑎 ≠ 𝑏, which of the following relations is correct? [A] 6 𝑅 3 [B] 6 𝑅 12 [C] 6 𝑅 27 [D] 6 𝑅 29 [E] 24 𝑅 12

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### Video Transcript

If set 𝑋 is equal to the numbers six, 12, 18, 24, 27, 29, 36 and 𝑅 is a relation on 𝑋, where 𝑎 𝑅𝑏 signifies that 𝑎 is twice 𝑏. Given that 𝑎 is an element of 𝑋, 𝑏 is an element of 𝑋, and 𝑎 is not equal to 𝑏, which of the following relations is correct?

We recall that a relation is a set of ordered pairs 𝑎, 𝑏. In this question, our value of 𝑎 must be twice the value of 𝑏. We can therefore immediately see that options (B), (C), and (D) cannot be correct. Six is not double 12, double 27, or double 29. In option (A), we see that six is double three. And in option (E), 24 is double 12.

We are also told in the question that the numbers (A) and (B) must be contained in set 𝑋. The numbers six, 12, and 24 are all contained in set 𝑋. However, the number three is not. This means that we can also eliminate option (A). The correct answer is, therefore, option (E) 24 𝑅 12.

Whilst it is not required in this question, the relation 𝑅 would actually contain three ordered pairs: the pairs 12, six; 24, 12; and 36, 18. This is because 12 is double six, 24 is double 12, and 36 is double 18. There are no other ordered pairs of numbers from set 𝑋 that would fit this relation.

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