Let's analyze the problem.

Question Analysis:

1. Statements Defined:

   • $p$: Kareem passes the final exam.
   • $q$: Kareem gets an A in the class.

2. Task (a):

   • Translate Rachel's statement "If Kareem passes the final exam, then Kareem will get an A in the class" into symbolic logic form.

   This is a conditional statement, which in symbolic form is written as: $p \rightarrow q$ This means "if $p$, then $q$."

3. Task (b):

   • Determine the truth values of $p$, $q$, and $p \rightarrow q$ based on a given situation.

   In the situation described:

   • Kareem didn't pass the final exam ($p = F$).
   • Kareem didn't get an A in the class ($q = F$).

   Truth Table Analysis for $p \rightarrow q$:

   • A conditional statement $p \rightarrow q$ is false only when $p = T$ and $q = F$.
   • For all other cases, it is true.

   In this case:

   • $p = F$, $q = F$ → $p \rightarrow q = T$.

Final Answers:

(a) Symbolic form of Rachel's statement: $p \rightarrow q$

(b) Truth values for the situation:

• $p = F$, $q = F$, $p \rightarrow q = T$.

Would you like a detailed explanation of conditional statements?

Related Questions:

1. What is the truth table for conditional statements?
2. Can you explain the logic behind $p \rightarrow q$ when $p = F$?
3. How does negation ($\sim p$) relate to conditionals?
4. How would the answer change if $p$ were true and $q$ false?
5. Can conditionals be represented in everyday language examples?

Tip:

Always remember, a conditional $p \rightarrow q$ is true when the hypothesis ($p$) is false, regardless of the conclusion ($q$).