Critical Thinking Quiz #7
Material conditional
______ ______ is the only thing that captures the invalidity of affirming the consequent and denying the antecedent
Material Conditional
a conditional that is false only when its antecedent is true and its consequent is false, otherwise its true
Well-formed formula (WFF)
a grammatically correct symbolic expression
Statement Variable
a lowercase letter that serves as a placeholder for any statement (p,q,r,s)
Material Biconditional
equivalent to a conduction of two material conditionals; its true when its constituent statements have the same truth value and false when they differ in truth value
Conditional
false if its antecedent true and consequent false, otherwise true
Minor logical operator
governs smaller components
Conjunction
if at least one is false, whole thing is false
Negation
if one is true, other is false. if one is false, other is true.
truth functional
its truth value is completely determined by the truth value of the atomic statements that compose it
Biconditional
just in case, necessary and sufficient condition
Atomic Statement
one that doesn't have any other statement as a component
Compound Statement
one that has at least one atomic statement as a component
Main logical operator
the one that governs the largest component or components of a compound statement
Biconditional
true if components have same truth value, or false
Disjunction
true, if at least one is true, otherwise is false
Syntax
vocabulary and grammer.
Negation
~
~ main logical operator . minor logical operator
~ (B . G) which is the main logical operator and which is the minor logical operator?
not
~ ; tilde
Conditional
->
if-then
-> ; arrow
Conjunction
.
and
. ; dot
Biconditional
<->
if and only if
<-> ; double arrow
Scheme of abbreviation
A list where we assign atomic statements to letters
Conjunction
Both the sky is blue and grass is green
Disjunction
Either the sky is blue or it is raining
Conditional
Given that, assuming that, provided that, on the condition that, if, only if
M -> A
Humans are animals if they are mammals
Conditional
If the sky is blue, then grass is green
Negation
It is not the case that the sky is blue
C v R
The crops will fail unless it rains
Disjunction
The sky is blue and/or it is raining; the sky is blue or it is raining; either the sky is blue or it is raining (or both); the sky is blue unless it is raining
Conjunction
The sky is blue but grass is green; the sky is blue however, grass is green; while the sky is blue, grass is green; although the sky is blue, grass is green.
Biconditional
The sky is blue if and only if grass is green
Negation
The sky is not blue; it is false that the sky is blue; it is not true that the sky is blue; the sky fails to be blue.
~ (R -> ~A)
The statement "if humans are rational, then they are not animals" is false
Disjunction
V
or
V ; vee
