Chapter 3, Problem 1RE

In Exercises 1-6, let p, q, and r represent the following simple statements:

p: The temperature is below 32°.

q: We finished studying.

r: We go to the movies.

Express each symbolic compound statement in English. If a symbolic statement is given without parentheses, place them, as needed, before and after the most dominant connective and then translate into English.

$p\wedge q\to r$

To determine

The provided symbolic statement $p\wedge q\to r$ into English statement.

Answer to Problem 1RE

Solution:

The English statement of the provided symbolic statement is

“$\underset{\_}{\text{The temperature is below 32}°\text{ and if studying is finished then go to the movies}\text{.}}$”

Explanation of Solution

Given:

Let p, q, and r represent the following simplestatements:

p: “The temperature is below $32°$.”

q: “We finished studying.”

r: “We go to the movies.”

If asymbolic statement is provided without parentheses, place them, asneeded, before and after the most dominant connective.

The provided symbolic statement is

$p\wedge q\to r$

Explanation:

To convert provided symbolic representation $p\wedge q\to r$ in English statement, use the parentheses to modify the provided statement. So,

$\left(p\wedge q\right)\to r$

where $\left(p\wedge q\right)\to r$ is a conditional statement whose ingredient variable is $\left(p\wedge q\right)$ with $r$.

$\left(p\wedge q\right)\to r$ is a conditional statement which is false only when antecedent is true and the consequent is false, and in rest all other cases, it is true.

$\left(p\wedge q\right)$ is a conjunction statement, and this will be true only when both of the variables $p$ and $q$ are true.

Hence, the English representation of modified symbolic statement is

The temperature is below $32°$ and if studying is finished then go to the movies.