Video Transcript
Using the Cartesian diagram below, determine the relation π times π. Is it (A) the set of ordered pairs one, one; two, one; one, six; and six, two? (B) The set of ordered pairs one, one; one, two; six, one; six, two. (C) The set of ordered pairs one, one; one, two; negative six, negative one; and negative six, negative two. (D) The set of ordered pairs negative one, negative one; negative one, negative two; negative six, negative one; and negative six, negative two. Or (E) the set of ordered pairs negative one, negative one; negative two, negative one; negative one, negative six; and negative six, negative two.
In this question, weβre given a Cartesian diagram and need to determine a Cartesian product. We recall that this Cartesian product is the set of all ordered pairs. Our diagram has four ordered pairs, as do each of the five options. All of these points lie in the first quadrant, which means that their π- and π-values must both be positive. This means we can rule out options (C), (D), and (E) as these all contain ordered pairs with negative coordinates.
The bottom-left point on our diagram has coordinates one, one. The point directly above this has coordinates one, two. Recalling that the π-coordinate comes first, we go along the π-axis to one and then up the π-axis to two. The bottom right of our four points has coordinates six, one as we go along the π-axis to six and up to one.
Finally, we have the point with coordinates six, two. The Cartesian product of π and π is the set of four ordered pairs one, one; one, two; six, one; and six, two. This means that the correct answer from our five options is (B). Option (A) is incorrect as the second and third ordered pair have the π- and π-coordinate the wrong way round.
