a declarative sentence that identifies as true or false. Never Both
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Declarative sentence
There's a subject and predicate.
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1
How would we denote or write TRUTH in propositions?
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0
How would we denote or write FALSE in propositions?
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Propositional variables
modify, combine, and relate propositions to each other with words such as "or", "and", "not", and "if-then" (v ^ \- -\>)
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Compound propositions
Also known as propositional functions. It also forms propositional variables (- v ^ -\>)
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-p
a negation of a proposition that represents and read as "not p"
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p ^ q
Read as: p and q
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Conjunction
True when BOTH statements are true (p ^ q)
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Conjunction
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p v q
Read as: p "or" q
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It is called disjunction
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Disjunction
compound statement that uses the word or
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Disjunction
at least there is ONE TRUE in the statements of p or q then it is TRUE
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Disjunction
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Conditional
Also known as implication. it is connected by "if....then" statements
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p -\> q
Read as: if p then q.
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it is called the Conditional or implication
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Conditional
It is FALSE when P is true and Q is false. Otherwise the rest of the statements will be TRUE
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Conditional
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Converse
q-\> p
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Inverse
~p --\> ~q (if not p then not q)
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Contrapositive
~q -\> ~p (if not q then not p)
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Exclusive OR
It is when EXACTLY ONE p or q is TRUE OR FALSE but not BOTH (it will be false)
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Exclusive OR
"one or the other but not both"
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⊕
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Exclusive OR
p⊕q is what
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p NAND q
p | q is?
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NAND
its only false if all operators (p and q) are true
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NAND
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NOR
It is TRUE when all operators (p and q) are false
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NOR
what is this called?
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Biimplication
It is considered TRUE when both operators have the same truth values
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Biimplication
what is this called? p
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p
symbol for "p if and only q" ?
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tautology
a compound proposition that is ALWAYS TRUE
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contradiction
a compound proposition that is ALWAYS FALSE
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Contingency
a compound proposition that is neither a tautology nor a contradiction
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biimplication
true only when both component operators have the same or identical truth value
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valid argument
a series of statements used to persuade someone.
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It presents reasons for them to accept a conclusion
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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.
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Indirect proof
a proof in which the statement to be proved is assumed to be false and a contradiction is shown
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Flashcard (20)