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Conjunction
Negation
Disjunction
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100

Construct the truth table for π‘βˆ§π‘ž

  • π‘‡βˆ§π‘‡=𝑇
  • π‘‡βˆ§πΉ=𝐹
  • πΉβˆ§π‘‡=𝐹
  • 𝐹∧𝐹=𝐹
100

Construct the truth table for ~p

|p|~p|

|T|F|

|F|T|

100

P is T, Q is T                

True both are true

100

A statement that is always true, no matter the truth values of its components.

What is a tautology?

100

This symbol (Β¬ or ~) is used to represent β€œnot” in logic.


What is conjunction?

200

Construct the truth table for Β¬π‘βˆ§π‘ž

Β¬π‘‡βˆ§π‘‡=πΉβˆ§π‘‡=𝐹

Β¬π‘‡βˆ§πΉ=𝐹∧𝐹=𝐹

Β¬πΉβˆ§π‘‡=π‘‡βˆ§π‘‡=𝑇

¬𝐹∧𝐹=π‘‡βˆ§πΉ

200

Construct a table for ~(~p)

|p|~p|~(~p)|

|T|F|T|
|F|T|F|

200

P is F, Q is T

True at least one

200

A statement that is always false, regardless of the truth values of its components.

What is a contradiction?

200

This symbol (∧) represents the logical operation meaning β€œand.”

What is conjunction?

300

Construct the truth table for Β¬π‘βˆ§Β¬π‘ž

Β¬π‘‡βˆ§Β¬π‘‡=𝐹∧𝐹=𝐹

Β¬T∧¬𝐹=πΉβˆ§π‘‡=𝐹

Β¬πΉβˆ§Β¬π‘‡=π‘‡βˆ§πΉ=𝐹

 Β¬πΉβˆ§Β¬πΉ=π‘‡βˆ§π‘‡=𝑇

300

Construct a table for (~(p/\q)|

| p | q | p /\ q | ~ ( p /\ q ) |

300

P is T, Q is F                  

False ( If P is T the -P is F. Now you have F \/ F, which is false.)

300

A column in a truth table that shows all possible truth values for a variable is called this.

What is a truth column?

300

This symbol (∨) represents the logical operation meaning β€œor.”

What is disjunction?

400

Construct the truth table for (π‘βˆ§π‘ž)βˆ§Β¬π‘

(π‘‡βˆ§π‘‡)βˆ§Β¬π‘‡=π‘‡βˆ§πΉ=𝐹

(π‘‡βˆ§πΉ)βˆ§Β¬π‘‡=𝐹∧𝐹=F 

(πΉβˆ§π‘‡)∧¬𝐹=πΉβˆ§π‘‡=𝐹

(𝐹∧𝐹)∧¬𝐹=πΉβˆ§π‘‡

400

| p | q | p \/ q | ~ ( p \/ q ) |

|T|T|T|F|

|T|F|T|F|

|F|T|T|F|

|F|F|F|T|

400

Two statements that always have the same truth values in every possible case are called this.

What are logically equivalent statements?

400

This symbol (β†’) is used to show β€œif…then” statements in logic.

What is implication?

500

Construct the truth table for (π‘βˆ§π‘ž)βˆ¨Β¬π‘ž

(π‘‡βˆ§π‘‡)βˆ¨Β¬π‘‡=π‘‡βˆ¨πΉ

500

Construct a table for ( ( ~ p ) \/ q)

| p | q | ~ p | (~p) \/ q |

|T|T|F|T|

|T|F|F|F|

|F|T|T|T|

|F|F|T|T|

500

The process of determining the truth value of a compound statement by listing all possibilities is called this.

Answer: What is constructing a truth table?

  

500

This double arrow symbol (↔) represents when two statements have the same truth value.

What is biconditional?