Questions: Suppose the following situation occurred. You didn't do all of the homework assignments. When you got your report card, you learned that you didn't pass the class. Complete the table to determine the truth of the teacher's statement in this situation. Use T for true and F for false. You may add more columns, but those added columns will not be graded.

Suppose the following situation occurred. You didn't do all of the homework assignments. When you got your report card, you learned that you didn't pass the class. Complete the table to determine the truth of the teacher's statement in this situation. Use T for true and F for false. You may add more columns, but those added columns will not be graded.
Transcript text: (b) Suppose the following situation occurred. You didn't do all of the homework assignments. When you got your report card, you learned that you didn't pass the class. Complete the table to determine the truth of the teacher's statement in this situation. Use $T$ for true and F for false. You may add more columns, but those added columns will not be graded.
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Solution

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Solution Steps

Step 1: Define the propositions

Let _p_ be the proposition "You do all the homework assignments." Let _q_ be the proposition "You pass the class."

The teacher's statement is "If you do all the homework assignments, then you will pass the class." This can be represented as _p_ → _q_.

The given situation is: "You didn't do all of the homework assignments" and "you didn't pass the class". This means _p_ is false and _q_ is false.

Step 2: Truth Table for Implication

The truth table for implication (→) is as follows:

| _p_ | _q_ | _p_ → _q_ | |---|---|---| | T | T | T | | T | F | F | | F | T | T | | F | F | T |

Step 3: Evaluate the teacher's statement

In the given situation, _p_ is false and _q_ is false. According to the truth table, when _p_ is false and _q_ is false, _p_ → _q_ is true.

Final Answer:

The teacher's statement is true in this situation. The completed table will have F under _p_, F under _q_, and T under _p_ → _q_.

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