### 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.