01 Logic and Quantifiers Free Online FlashCards

What is a proposition?

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

When is $p\land q$ true?

It is true exactly when both component propositions are true.

What does $p\lor q$ mean?

It is true when at least one component proposition is true, including when both are true.

When is $p\to q$ false?

It is false only when $p$ is true and $q$ is false; otherwise it is true.

When is $p\leftrightarrow q$ true?

It is true exactly when $p$ and $q$ have the same truth value.

How many rows does a complete truth table need?

A complete truth table has $2^n$ rows when it contains $n$ distinct propositions.

What is the logical operator precedence order?

The precedence order is $\neg$, then $\land$, then $\lor$, then $\to$, then $\leftrightarrow$.

What is a tautology?

A tautology is a proposition that is true under every possible assignment of truth values.

Simplify $\neg(p\lor\neg q)$.

By De Morgan’s law, $\neg(p\lor\neg q)\equiv\neg p\land q$.

What is a predicate?

A predicate is a statement involving variables whose truth depends on assigned values and the domain.

What does $\forall$ mean?

The universal quantifier $\forall$ means “for every” or “for all” elements in the stated domain.

What does $\exists$ mean?

The existential quantifier $\exists$ means that at least one element of the domain satisfies the predicate.