5. Let P be the statement \"Student X passed every assignment in Calculus I,\" a

Question

5. Let P be the statement "Student X passed every assignment in Calculus I," and let Q be the statement "Student X received a grade of C or better in (a) What does it mean for P to be true? What does it mean for Q to be (b) Suppose that Student X passed every assignment in Calculus I and Calculus I." true? received a grade of B-, and that the instructor made the statement P ? Q. Would you say that the instructor lied or told the truth? (c) Suppose that Student X passed every assignment in Calculus I and received a grade of C-, and that the instructor made the statement P . Would you say that the instructor lied or told the truth? (d) Now suppose that Student X did not pass two assignments in Calculus I and received a grade of D, and that the instructor made the statement P-Q. Would you say that the instructor lied or told the truth? (e) How are Parts (5b), (5c), and (5d) related to the truth table for P-Q?

Explanation / Answer

a. If P is true then student X turned in all assignments in Calculus I. If Q is true then student X received a grade of C or better in Calculus I

b.  The instructor told the truth as P ? Q is true if both P and Q are true.

c.  The instructor lied because if P is true and Q is false then P ? Q is false

d. The instructor did not lie as the student did not turn in all assignments, the instructor did not have to give a grade of at least C to be truthful. This is equivalent to the truth of the statement P ? Q when both are false

e. They are precisely the truths and falsehood for P ? Q when both are true, when P is true and Q is false, and when both are false

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