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Symbolic Notation Practice

Authored by Sarah Dulaney

Mathematics

9th - 12th Grade

CCSS covered

Used 17+ times

Symbolic Notation Practice
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8 questions

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1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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)

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

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