Questions: Suppose the following situation occurred. You got a flu shot. During the winter, you got the flu. Complete the table to determine the truth of the clinic'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. p q p → ~q Your answer from part (a) will fill in here. p 9 ㅁㅁ ~ ロ^口 → 6

Suppose the following situation occurred. You got a flu shot. During the winter, you got the flu.

Complete the table to determine the truth of the clinic'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.
p
q
p → ~q
Your answer from part (a)
will fill in here.

p 9 ㅁㅁ
~ ロ^口
→ 6

Transcript text: Suppose the following situation occurred. You got a flu shot. During the winter, you got the flu. Complete the table to determine the truth of the clinic'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. $p$ $q$ $p \rightarrow \sim q$ Your answer from part (a) will fill in here. \begin{tabular}{|c|c|c|} \hline p & 9 & \multirow[b]{2}{*}{ㅁㅁ} \\ \hline $\sim \square$ & ロ^口 & \\ \hline $\square \rightarrow \square$ & $\square \multimap \square$ & \\ \hline $\times$ & & 6 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Define the propositions

p: You got a flu shot. q: You got the flu.

Step 2: Determine the truth values of p and q

Since the problem states "You got a flu shot" and "you got the flu," both p and q are true.

Step 3: Evaluate the truth value of ¬p → ¬ q

¬p: You did not get a flu shot (False) ¬q: You did not get the flu (False) ¬p → ¬q: If you did not get a flu shot, then you did not get the flu. (True) A conditional statement is only false when the hypothesis is true, and the conclusion is false.