2/9 2. Logical Connectives and Symbolic Translation Free Online FlashCards

What is a proposition?

A proposition is a declarative sentence that is either true or false, but not both.

What is a compound statement?

A compound statement combines propositions using one or more logical connectives.

What does $\lnot p$ mean?

$\lnot p$ is the negation of $p$; it reverses $p$'s truth value.

When is $p \land q$ true?

$p \land q$ is true only when both $p$ and $q$ are true.

What does standard $p \lor q$ allow?

$p \lor q$ is true when at least one proposition is true, including when both are true.

When is $p \to q$ false?

A conditional $p \to q$ is false only when $p$ is true and $q$ is false.

Identify the parts of $p \to q$.

In $p \to q$, $p$ is the antecedent and $q$ is the consequent.

How is “$p$ only if $q$” symbolized?

“$p$ only if $q$” translates as $p \to q$.

What are the converse, inverse, and contrapositive of $p \to q$?

For $p \to q$, the converse is $q \to p$, the inverse is $\lnot p \to \lnot q$, and the contrapositive is $\lnot q \to \lnot p$.

How can $p \leftrightarrow q$ be expressed using conditionals?

$p \leftrightarrow q$ means $(p \to q) \land (q \to p)$.

When is $p \leftrightarrow q$ true?

A biconditional is true when its two propositions have the same truth value: both true or both false.

Translate a conditional with a conjunctive antecedent.

The statement “If the store is open and I have enough money, then I will buy the item” becomes $(p \land q) \to r$.