WEBVTT
00:00:01.920 --> 00:00:17.120
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.
00:00:18.120 --> 00:00:27.800
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?
00:00:29.040 --> 00:00:34.520
We recall that a relation is a set of ordered pairs 𝑎, 𝑏.
00:00:35.360 --> 00:00:38.760
In this question, our value of 𝑎 must be twice the value of 𝑏.
00:00:39.320 --> 00:00:45.960
We can therefore immediately see that options (B), (C), and (D) cannot be correct.
00:00:46.760 --> 00:00:54.680
Six is not double 12, double 27, or double 29.
00:00:55.600 --> 00:00:59.240
In option (A), we see that six is double three.
00:00:59.720 --> 00:01:04.040
And in option (E), 24 is double 12.
00:01:05.160 --> 00:01:10.400
We are also told in the question that the numbers (A) and (B) must be contained in set 𝑋.
00:01:11.360 --> 00:01:16.240
The numbers six, 12, and 24 are all contained in set 𝑋.
00:01:16.960 --> 00:01:19.320
However, the number three is not.
00:01:19.960 --> 00:01:23.080
This means that we can also eliminate option (A).
00:01:23.760 --> 00:01:29.640
The correct answer is, therefore, option (E) 24 𝑅 12.
00:01:30.800 --> 00:01:44.880
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.
00:01:45.440 --> 00:01:54.840
This is because 12 is double six, 24 is double 12, and 36 is double 18.
00:01:55.520 --> 00:02:02.040
There are no other ordered pairs of numbers from set 𝑋 that would fit this relation.