Symbolic Notation Practice

Let p be: "Federer wins his match."

Let q be: "Nadal does not win his match."

What is p ∧ q?

• Federer wins his match and Nadal does not win his match.

• Federer wins his match or Nadal does not win his match.

• Federer does not win his match and Nadal wins his match.

• If Ferderer wins his match, then Nadal does not win his match.

Answer explanation

p ∧ q means p AND q (hypothesis and conclusion)

Tags

CCSS.HSS.CP.A.1

Let p be: "I vacuum the house."

Let q be: "I get my allowance."

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: "The air conditioner is working."

Let q be: "The apartment is hot."

What is ~q → p?

• If the air conditioner is not working, then the apartment is hot.

• If the apartment is hot, then the air conditioner is working.

• If the air conditioner is working, then the apartment is not hot.

• If the apartment is not hot, then the air conditioner is working.

Answer explanation

~q → p means "if not q, then p"

Tags

CCSS.7.SP.C.8B

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).

Tags

CCSS.HSS.CP.A.3

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.

Tags

CCSS.7.SP.C.8B

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.

Tags

CCSS.HSS.CP.A.1

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).

Tags

CCSS.HSS.CP.A.3

Let p be: "Jimmy makes dinner."

Let q be: "Andrew sets the table."

What is q → p?

• If Jimmy makes dinner, then Andrew sets the table.

• If Andrew sets the table, then Jimmy makes dinner.

• If Jimmy does not make dinner, then Andrew does not set the table.

• If Andrew does not set the table, then Jimmy does not make dinner.

Answer explanation

q → p is the converse (conclusion followed by the hypothesis)