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Intermediate Logic Comp. Questions Lessons 1-5
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T or F: One proposition may be expressed by many different sentences.
True
Words that combine or modify simple propositions to make compound propositions (and; or) are called_______. They are like __________.
logical operators: conjunctions
Which one is a truth-functional proposition: "It is false that God loves the world" or "I believe in Santa"? Why?
The 1st is truth-functional b/c it depends on the truth value of "God loves the world". 2nd = self-report that is generally regarded as true.
A simple proposition cannot be represented by ____ ____ _____ constant.
more than one
A single constant or variable can represent either _____ or ____ propositions.
simple; compound
Three fundamental logical operators are:
Negation, conjunction, and disjunction
The negation of a proposition is also the _____________ of that proposition.
Contradiction
Contradiction is the relationship between ___ & ___ stmts.
A & O, E and I
The conjunction sign can mean _____, _____, or ______.
and, but or still
A conjunction is true _____________
if and only if both conjuncts are true.
The disjunction is usually an "inclusive or" which means _____ _____ __ ______. An exclusive or means ____ ____ ___ ___ ____.
This or that, or both: This or that, but not both.
How would "the senator is either a Republican or a Democrat" be translated (meaning the exclusive "or")? How is this spoken?
(R∨D)∙∼(R∙D) "The senator is either a Republican or a Democrat, but not both a Republican and a Democrat."
A disjunction is true if ______________ AND is considered false if and only if ______________________________________________.
either disjunct is true: both disjuncts are false.
In a series of 3+ connected propositions, _________ should be used to avoid ambiguity.
parenthesis
In the absense of parenthesis, assume that negation attaches only to the proposition __ _________________________.
it immediately precedes
When "not" comes before "both", the tilde goes _________, so "cats &dogs are not both mammals" is symbolized:
before the parenthesis: ∼(C∙S)
When "both" comes before "not", the tilde goes _________, so "both cats & snakes are not mammals" is symbolized:
afterthe parenthesis: (∼C∙∼S)
(∼C∙∼S) can be read either________ or ________.
"both cats and snakes are not mammals" or "neither cats nor snakes are mammals."
∼p ∨ q would be translated
not p... or q?????
∼(p ∨ q) would be translated
not p or not q??????
A conditional is false ___________...
if and only if the antecedent is true and the consequent is false.
p ⊃ q is equivalent to
∼(p ∙ ∼q)
Translate p ⊃ q five different was:
if p then q
p implies q
p only if q
when p, q
p is sufficient for q
q ⊃ p
p if q
q ⊃ p
p is necessary for q
∼q ⊃ p
p unless q
∼p ⊃ q
unless p, q
The biconditional is true ___ otherwise _____.
when both component propositions have the same truth value: it is false.
p ≡ q is equivalent to
(p ⊃ q) ∙ (q ⊃ p)
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