QuestionSymbolically express: If not $p$ , then not $q$ .

Studdy Solution

STEP 1

Assumptions1. $p$ represents the statement "This is a crocodile." . $q$ represents the statement "This is a reptile."

STEP 2

The given compound statement is "If this is not a crocodile, then this is not a reptile." We can write this in the form "If not $p$ , then not $q$ ."

STEP 3

In symbolic form, "not $p$ " is represented as $\neg p$ and "not $q$ " is represented as $\neg q$ .

STEP 4

The conditional statement "If $p$ , then $q$ " is represented symbolically as $p \rightarrow q$ .

STEP 5

Substituting $\neg p$ for $p$ and $\neg q$ for $q$ in the conditional statement gives us the symbolic form of the given compound statement.
$\neg p \rightarrow \neg q$ So, the compound statement "If this is not a crocodile, then this is not a reptile." can be written in symbolic form as $\neg p \rightarrow \neg q$ .

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