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.

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 $\square$
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Solution

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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: $I get a raise \leftrightarrow I work hard$.

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