Symbolic Notation

What is q ⟷ p?

• If I vacuum the house, then I get my allowance.

• I vacuum the house if and only if I get my allowance.

• I get my allowance if and only if I vacuum the house.

• If I do not vacuum the house, then I do not get my allowance.

Answer explanation

q ⟷ p is a biconditional statement (q if and only if p)

Let p be: "I run every day."

Let q be: "I make the track team."

Represent "If I do not make the track team, then I did not run every day."

• p → q

• q → p

• ~p → ~q

• ~q → ~p

Answer explanation

"If I do not make the track team, then I did not run every day" has negated both the hypothesis and the conclusion and reversed their order (contrapositive).

Let p be: "I run every day." Let q be: "I make the track team." Represent "I will make the track team if and only if I run every day."

• p → q

• q → p

• q ⟷ p

• p ⟷ q

Answer explanation

"I will make the track team if and only if I run every day" is a biconditional statement, which uses a double arrow.

Let p be: "I run every day." Let q be: "I make the track team." Represent "I run every day, therefore I make the track team."

• p ∴ q

• q ∴ p

• p ∨ q

• p ∧ q

Answer explanation

Using "therefore" will require the symbol of the three dots.

Let p be: "I run every day." Let q be: "I make the track team." Represent "If I do not run every day, then I do not make the track team."

• p → q

• q → p

• ~p → ~q

• ~q → ~p

Answer explanation

"If I do not run every day, then I do not make the track team" has negated both statements, but keeps the hypothesis and conclusion in their original order (inverse).

What does this symbol mean?

• If__, then___.

• negation (not)

• therefore

• if and only if

What does this symbol mean?

• negation (not)

• therefore

• and

• or

What does this symbol mean?

• If___, then___.

• negation (not)

• therefore

• if and only if

What does this symbol mean?

• negation (not)

• therefore

• and

• or

What does this symbol mean?

• If___, then___.

• negation (not)

• therefore

• if and only if