Questions: Let p and q represent the following simple statements.
p : I get a raise.
q: I work hard.
Write the following compound statement in symbolic form.
I get a raise if and only if I work hard.
The compound statement written in symbolic form is p if and only if q.
Transcript text: Let $p$ and $q$ represent the following simple statements.
p : I get a raise.
q: I work hard.
Write the following compound statement in symbolic form.
I get a raise if and only if I work hard.
The compound statement written in symbolic form is $\square$
Solution
Solution Steps
Step 1: Identify the simple statements
The simple statements are identified as: $p$ for "I get a raise" and $q$ for "I work hard".
Step 2: Determine the logical structure
The logical structure is determined by the operator: "if and only if".
Step 3: Translate to symbolic form
The compound statement in symbolic form is: $I get a raise \leftrightarrow I work hard$.
Final Answer:
The symbolic representation of the compound statement is: $I get a raise \leftrightarrow I work hard$.