Questions: Consider the following partial grade book for a certain class. - Name Midterm Score - Maudie 87 - Truman 68 - Vera 75 Consider the set A = Maudie, Truman, Vera and B = 87,68,75. Then consider the relation R from A to B consisting of pairs (a,b) from the table above with a in A and b in B. In listing all the pairs of R, we have (87, Maudie), (81, Truman), (77, Vera). True False

Consider the following partial grade book for a certain class. - Name Midterm Score - Maudie 87 - Truman 68 - Vera 75 Consider the set A = Maudie, Truman, Vera and B = 87,68,75. Then consider the relation R from A to B consisting of pairs (a,b) from the table above with a in A and b in B. In listing all the pairs of R, we have (87, Maudie), (81, Truman), (77, Vera). True False
Transcript text: Consider the following partial grade book for a certain class. \begin{tabular}{|l|l|} \hline Name & Midterm Score \\ \hline Maudie & 87 \\ \hline Truman & 68 \\ \hline Vera & 75 \\ \hline \end{tabular} Consider the set $\mathrm{A}=\{$ Maudie, Truman, Vera $\}$ and $\mathrm{B}=\{87,68,75\}$. Then consider the relation R from A to B consisting of pairs (a,b) from the table above with $a \in A$ and $b \in B$. In listing all the pairs of R, we have $\{(87$, Maudie), $(81$, Truman), $(77$, Vera $)\}$. True False
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Solution

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Solution Steps

To determine if the given statement about the relation \( R \) is true or false, we need to verify if the pairs listed in the statement match the pairs derived from the grade book. The relation \( R \) should consist of pairs where the first element is a name from set \( A \) and the second element is the corresponding score from set \( B \). We will compare the given pairs with the correct pairs derived from the table.

Step 1: Define the Sets

We have the sets \( A = \{ \text{Maudie}, \text{Truman}, \text{Vera} \} \) and \( B = \{ 87, 68, 75 \} \). The relation \( R \) consists of pairs \( (a, b) \) where \( a \in A \) and \( b \in B \).

Step 2: Establish the Correct Relation

The correct relation \( R \) based on the grade book is: \[ R = \{ (\text{Maudie}, 87), (\text{Truman}, 68), (\text{Vera}, 75) \} \]

Step 3: Analyze the Given Relation

The given relation in the problem statement is: \[ \text{Given Relation} = \{ (87, \text{Maudie}), (81, \text{Truman}), (77, \text{Vera}) \} \] We can see that the pairs do not match the correct relation. Specifically, the scores \( 81 \) and \( 77 \) do not correspond to any of the students in set \( A \).

Step 4: Conclusion

Since the pairs in the given relation do not match the correct pairs derived from the grade book, we conclude that the statement is false.

Final Answer

\(\boxed{\text{False}}\)

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