Question

name
date
period
geometry
unit 2: logic & proof
quiz 2.1: statements, compound, and conditionals
determine if the conjecture below are true or false. if false, give a counterexample.
1.
4.
8.
match each statement with its symbolic notation.

1. conjunction a. ( q \to p )

b. disjunction b. ( p leftrightarrow q )

1. conditional c. ( p vee q )
2. biconditional d. (

eg p \to
eg q )

1. contrapositive e. (

eg q \to
eg p )

1. converse f. ( p wedge q )
2. inverse g. ( p \to q )

use the statements below to write compound statements. then, determine the truth value.
p: atlanta is the capital of georgia.
q: there are 4 feet in a yard.

1. ( p vee q ):

truth value:

1. ( p wedge q ):

truth value:

1. ( p wedge

eg q ):
truth value:

1. (

eg p vee q ):
truth value:
© gina wilson (all things algebra), llc), 2014 - 2018

Explanation:

Step1: Analyze statement \( p \) and \( q \)

• \( p \): Atlanta is the capital of Georgia (True, as Atlanta is the capital of Georgia).
• \( q \): There are 4 feet in a yard (False, as there are 3 feet in a yard, so \(

eg q \) is True).

Step2: Solve \( p \vee q \)

• \( p \vee q \) means "Atlanta is the capital of Georgia or there are 4 feet in a yard".
• In logic, a disjunction (\( \vee \)) is true if at least one of the statements is true. Since \( p \) is true, \( p \vee q \) is true.

Step3: Solve \( p \wedge q \)

• \( p \wedge q \) means "Atlanta is the capital of Georgia and there are 4 feet in a yard".
• A conjunction (\( \wedge \)) is true only if both statements are true. Since \( q \) is false, \( p \wedge q \) is false.

Step4: Solve \( p \wedge

eg q \)

• \(

eg q \) is "There are not 4 feet in a yard" (which is true).

• \( p \wedge

eg q \) means "Atlanta is the capital of Georgia and there are not 4 feet in a yard".

• Both \( p \) and \(

eg q \) are true, so the conjunction is true.

Step5: Solve \(

eg p \vee q \)

• \(

eg p \) is "Atlanta is not the capital of Georgia" (false).

• \(

eg p \vee q \) means "Atlanta is not the capital of Georgia or there are 4 feet in a yard".

• A disjunction is true if at least one is true, but both \(

eg p \) and \( q \) are false, so \(
eg p \vee q \) is false.

Answer:

s:

1. \( p \vee q \): Atlanta is the capital of Georgia or there are 4 feet in a yard; Truth Value: True
2. \( p \wedge q \): Atlanta is the capital of Georgia and there are 4 feet in a yard; Truth Value: False
3. \( p \wedge

eg q \): Atlanta is the capital of Georgia and there are not 4 feet in a yard; Truth Value: True

1. \(

eg p \vee q \): Atlanta is not the capital of Georgia or there are 4 feet in a yard; Truth Value: False