R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2, V2) if and only if (1) x < x, or (2) x, = x, & y, < y2. Prove that < defines a linear ordering on the set of ordered pairs of real numbers. (This shows that the coordinate plane can be linearly ordered!)

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Q: For this one can you please explain to me How does number 1 is differ from a relation?

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A: I am attaching image so that you understand each and every step.

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A: Given query is to graph the inequality.

Q: Please help me with these questions. I am having trouble understanding what to do Thank you

A: Step 1 1) Definition of R1​ and R3​: R1​ = { (a, b) ∈ R2 ∣ a &gt; b }   (greater than relation)R3 =…

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A: Consider the points given on the graph: -4,2  and  4,-2 Plot the points on the coordinate axis:

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