Questions: Using logic to test a claim: Conditional statement, advanced Your dentist gave you this statement as advice at your last visit. If you don't brush your teeth twice a day and you don't floss every day, then you will get a cavity this year, (a) Statements p, q, and r are defined as follows. p: You brush your teeth twice a day, q: You floss every day. r: You get a cavity this year. Write the dentist's statement in symbolic form using p, q, and r, Symbolic form: (b) Suppose the following situation occurs, You don't brush your teeth twice a day and you don't floss every day. And you don't get a cavity this year. Based on this situation, complete the table to determine the truth of the dentist's statement. Use T for true and F for false, You may add more columns to the table, but those added columns will not be graded.

Solution Steps

• \( p \): You brush your teeth twice a day.
• \( q \): You floss every day.
• \( r \): You get a cavity this year.

The given statement is: "If you don’t brush your teeth twice a day and you don’t floss every day, then you will get a cavity this year."

In symbolic form, this can be written as: \[ (\neg p \land \neg q) \rightarrow r \]

Construct a truth table to determine the truth values of the statement \( (\neg p \land \neg q) \rightarrow r \).

| \( p \) | \( q \) | \( r \) | \( \neg p \) | \( \neg q \) | \( \neg p \land \neg q \) | \( (\neg p \land \neg q) \rightarrow r \) | |--------|--------|--------|--------------|--------------|--------------------------|------------------------------------------| | T | T | T | F | F | F | T | | T | T | F | F | F | F | T | | T | F | T | F | T | F | T | | T | F | F | F | T | F | T | | F | T | T | T | F | F | T | | F | T | F | T | F | F | T | | F | F | T | T | T | T | T | | F | F | F | T | T | T | F |

Final Answer