Conjunction
Negation
Disjunction
Vocab
Symbols
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

 In logic, this type of disjunction, often represented by the word "or", is true if at least one of the components is true.

What is an inclusive disjunction

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

In genetics, this failure of chromosomes to separate properly during meiosis often leads to disorders like Trisomy 13.

What is Non-disjunction

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?

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