PHIL 150 Chapter Notes - Chapter 7, A-B: Wednesday, Necessity And Sufficiency, Exclusive Or
10 May 2018
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LOGIC Reading Notes
Chapter 7: Propositional Logic (A-B)
A. Logical Operators and Translators
x Logical operators: special symbols that can be used as part of ordinary language statement
translations
x Propositional logic: the basic components in propositional logic are statements
o In categorical logic, the basic components were class terms
x Simple statement: one that does not have any other statement or logical operator as a component
o Ex: Wednesday is hump day
o Statement – sentence with a truth value
x Compound statement: a statement that has at least one simple statement and at least one logical
operator as components
Operator
Name
Compound Type
Used to translate
~
Tilde
Negation
It is not the case that
Dot
Conjunction
And; also; moreover
V
Wedge
Disjunction
Or; unless
Horseshoe
Conditional
If…then…; only if
Triple bar
Biconditional
If and only if
x Negation: the word not and the phrase it is not the case that are used to deny the statement
that follows them, and we refer to their use as negation
x Ex: It is not the case that drinking hot coffee reduces sweating.
o It is not the case that D.
o ~ D
x Conjunction: a compound statement that has two distinct statements (called conjuncts) connected
by the dot symbol
o Ex:
Hamlet
is a tragedy and
Kung Fu Panda
is a comedy.
▪ H and K
▪ H K
x Disjunction: a compound statement that has two distinct statements (called disjuncts) connected
by the wedge symbol
o Ex: Unless it rains today, we will go swimming.
▪ R v S
x Inclusive disjunction: a compound statement which both disjuncts can be true at the same time
o Ex: Either July or August has 31 days.
x Exclusive disjunction: a compound statement in which both disjuncts cannot be true at the same
time
o Ex: You can have either soup or salad with your meal.
▪ (S v A) ~ (S F)
o The wedge symbolizes inclusive disjunction
x Conditional statement: in ordinary language, the word if typically precedes the antecedent of a
conditional, and the statement that follows the word then, is referred to as the consequent
o Antecedent Consequent
o Ex: In the event of P, then Q.
▪ P Q
o Ex: P implies Q.
▪ P Q
o Distinguishing between if and only if
o Ex: Only if she has a 10% down payment will she get a mortgage.
▪ M P
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