math logic from quizlet

Logic

the process and science of reasoning

Propositions

a declarative sentence that identifies as true or false. Never Both

Declarative sentence

There's a subject and predicate.

1

How would we denote or write TRUTH in propositions?

0

How would we denote or write FALSE in propositions?

Propositional variables

modify, combine, and relate propositions to each other with words such as "or", "and", "not", and "if-then" (v ^ \- -\>)

Compound propositions

Also known as propositional functions. It also forms propositional variables (- v ^ -\>)

-p

a negation of a proposition that represents and read as "not p"

p ^ q

Read as: p and q

Conjunction

True when BOTH statements are true (p ^ q)

Conjunction

p v q

Read as: p "or" q

It is called disjunction

Disjunction

compound statement that uses the word or

Disjunction

at least there is ONE TRUE in the statements of p or q then it is TRUE

Disjunction

Conditional

Also known as implication. it is connected by "if....then" statements

p -\> q

Read as: if p then q.

it is called the Conditional or implication

Conditional

It is FALSE when P is true and Q is false. Otherwise the rest of the statements will be TRUE

Conditional

Converse

q-\> p

Inverse

~p --\> ~q (if not p then not q)

Contrapositive

~q -\> ~p (if not q then not p)

Exclusive OR

It is when EXACTLY ONE p or q is TRUE OR FALSE but not BOTH (it will be false)

Exclusive OR

"one or the other but not both"

⊕

Exclusive OR

p⊕q is what

p NAND q

p | q is?

NAND

its only false if all operators (p and q) are true

NAND

NOR

It is TRUE when all operators (p and q) are false

NOR

what is this called?

Biimplication

It is considered TRUE when both operators have the same truth values

Biimplication

what is this called? p

p

symbol for "p if and only q" ?

tautology

a compound proposition that is ALWAYS TRUE

contradiction

a compound proposition that is ALWAYS FALSE

Contingency

a compound proposition that is neither a tautology nor a contradiction

biimplication

true only when both component operators have the same or identical truth value

valid argument

a series of statements used to persuade someone.

It presents reasons for them to accept a conclusion

Conditional proof

A deduction for a conditional claim "If P, then Q" that proceeds by assuming that P is true and then proving that, on that assumption, Q must also be true.

Indirect proof

a proof in which the statement to be proved is assumed to be false and a contradiction is shown

Fallacies

error in reasoning. invalid argument