2.2 Compound Statements

Joining simple statements with and, or, and if-then, unpacking parenthesized symbolic forms into English, and the dominance order of connectives.

Contemporary Mathematics, 2.2 Compound Statements

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4 exercises

2.2 Exercise 1

For each of the following connectives, write its name and associated symbol.

or
implies
but

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2.2 Exercise 3

Let $p$ represent the statement, “It is a warm sunny day,” and let $q$ represent the statement, “the family will go to the beach.” Write the symbolic form of each of the following compound statements.

If it is a warm sunny day, then the family will go to the beach.
The family will go to the beach, and it is a warm sunny day.
The family will not go to the beach if and only if it is not a warm sunny da…

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2.2 Exercise 5

Let $p$ represent the statement, “My child finished their homework,” let $q$ represent the statement, “My child cleaned her room,” let $r$ represent the statement, “My child played video games,” and let $s$ represent the statement, “My child streamed a movie.” Translate each of the following symbolic statements into words.

$\sim \left(p \land q\right)$
$\left(p \land q\right) \rightarrow \left(r \lor s\right)$
$\sim \left(r \lor s\right) \leftrightarrow \sim \left(p \land q\right)$

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2.2 Exercise 7

For each of the following compound logical statements, add parentheses to indicate the order to evaluate the statement. Recall that parentheses are evaluated innermost first.

$p \land \sim q \lor r$
$q \rightarrow \sim p \land r$
$\sim \left(p \lor q\right) \leftrightarrow \sim p \land \sim q$

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