Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 22, 2023

Write a compound statement in symbolic form: The store is not closed if and only if it is not Sunday. $\neg p \leftrightarrow \neg q$

STEP 1

Assumptions1. The simple statement $p$ represents "It is Sunday." . The simple statement $q$ represents "The store is closed."
3. The compound statement we are trying to represent is "The store is not closed if and only if it is not Sunday."

STEP 2

We need to understand the structure of the compound statement. The statement "The store is not closed if and only if it is not Sunday" is a biconditional statement. In symbolic form, a biconditional statement is represented as $p \iff q$ .

STEP 3

Now, we need to represent the negations in the statement. The phrase "not Sunday" is the negation of the statement $p$ , and it is represented as $\neg p$ .

STEP 4

Similarly, the phrase "The store is not closed" is the negation of the statement $q$ , and it is represented as $\neg q$ .

STEP 5

Now, we can combine the symbols from steps3 and4 to represent the entire compound statement. The compound statement "The store is not closed if and only if it is not Sunday" can be represented as $\neg q \iff \neg p$ .
The compound statement written in symbolic form is $\neg q \iff \neg p$ .

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