Question

determine if the relations $r_1 = \\{(0, -4), (2, -1), (3, 1), (4, 2), (3, 5)\\}$ and $r_1 = \\{(-4, 0), (-1, 2), (0, 3), (1, 4), (5, 3)\\}$ are inverses. (1 point)

\bigcirc no, not all corresponding ordered pairs are reflections of one another in the line $y = -x$.

\bigcirc yes, all corresponding ordered pairs are reflections of one another in the line $y = x$.

\bigcirc no, not all corresponding ordered pairs are reflections of one another in the line $y = x$.

\bigcirc yes, all corresponding ordered pairs are reflections of one another in the line $y = -x$.

Explanation:

Step1: Recall Inverse Relation Rule

For two relations to be inverses, if \((a,b)\) is in \(R_1\), then \((b,a)\) should be in \(R_2\) (reflection over \(y = x\)).

Step2: Check Each Pair in \(R_1\)

• For \((0, - 4)\) in \(R_1\), check \(R_2\): \(R_2\) has \((-4,0)\) – good.
• For \((2, - 1)\) in \(R_1\), check \(R_2\): \(R_2\) has \((-1,2)\) – good.
• For \((3,1)\) in \(R_1\), check \(R_2\): \(R_2\) has \((1,4)\) (not \((1,3)\)) – bad.
• For \((4,2)\) in \(R_1\), check \(R_2\): \(R_2\) has \((0,3)\) (not \((2,4)\)) – bad.
• For \((3,5)\) in \(R_1\), check \(R_2\): \(R_2\) has \((5,3)\) – good.

Since not all pairs in \(R_1\) have their \((b,a)\) in \(R_2\) (reflection over \(y = x\)), the answer is the option about not all over \(y = x\).

Answer:

C. No, not all corresponding ordered pairs are reflections of one another in the line \(y = x\) (assuming the third option is labeled C, adjust label as per original, but the content is "No, not all corresponding ordered pairs are reflections of one another in the line \(y = x\)")