Pure Math Unit 1 Logic and Reasoning

Negation/ ”Not”

not

Conjunction/ “And”

and

Disjunction/ “Or”

or

Conditional/ “if _ then _” / ”_ implies _”

“if _ then _” / ”_ implies _”

Bi-Condional/ ”__ if and only if __”

__ if and only if __

What is the rule for Negation/”Not”?

the prepositions’ values become the opposite: T becomes F and F becomes T.

What is the rule for Conjunction/”And” ?

Both prepositions (p and q) must be true/have T to give true.

What is the rule for Disjunction/”Or”?

there must be at least one T between both p and q in order to be true

What is the rule for Conditional/“if _ then _” / ”_ implies _”?

True every time except when the first preposition is true and the second preposition is false.

False only when the first preposition is true and the second preposition is false, otherwise it is true every time.

What is the rule for Bi-Conditional/”__ if and only if __”?

True only when both prepositions/values are the same.

What is a Tautology?

A tautology is a compound statement that is always true.

What is a contradiction?

A contradiction is a compound statement that is always false.

What is a contingency?

A contingency is a compound statement that is neither fully true or fully false.

What does “logically equivalent mean”

Two statements are logically equivalent when they have the exact same truth table values/results

What does converse mean?

The converse is when the prepositions switch places: the preposition to the left of the symbol moves to the right and the preposition that was on the right of the sign moves to the left.

What does inverse mean?

The inverse means that the prepositions change signs: prepositions without a negation sign, get a negation sign (~) and prepositions with a negation sign (~), remove the negation sign.

What does the contrapositive mean?

The contrapositive mean that both the converse (prepositions swap/trade places) and the inverse (prepositions change to the oppositie sign) take place.