M4S2 Flashcards
“And” statement is TRUE only when
BOTH subsentences are TRUE.
An `or’ sentence is true when
at least
one of the subsentences is TRUE
An `exclusive-or’ statement is
true when
only one of the
subsentences is TRUE.
Converse proposition:
𝒒 → p
Inverse proposition:
~𝒑 → ~q
Contrapositive proposition:
~𝒒 → ~p
“If today is Thursday, then I have a test today.”
Converse:
“If I have a test today, then today is Thursday.”
“If today is Thursday, then I have a test today.”
Inverse:
“If today is not Thursday then I do not have test today.
“If today is Thursday, then I have a test today.”
Contrapositive:
“If I do not have a test today, then today is not Thursday.”
Two statements are equivalent in a biconditional statement when they
have the
SAME truth values.
Two statements are said to be logically equivalent if
they
have the same truth value for every possible cases.
𝒑 ∧ 𝑻== 𝒑
𝒑 ∨ 𝑭==𝒑
Identity laws
𝒑 ∨ 𝑻==𝑻
𝒑 ∧ 𝑭==𝑭
Domination laws
𝒑 ∨ 𝒑 <=> 𝒑
𝒑 ∧ 𝒑 <=> 𝒑
Idempotent laws
~(~𝒑) == 𝒑
Double negation laws
𝒑 ∨ 𝒒 <=> 𝒒 ∨ 𝒑
𝒑 ∧ 𝒒 <=> 𝒒 ∧ 𝒑
Commutative laws
(𝒑 ∨ 𝒒) ∨ 𝒓
𝒑 ∨ (𝒒 ∨ 𝒓)
(𝒑 ∧ 𝒒 ) ∧ 𝒓
𝒑 ∧ (𝒒 ∧ 𝒓)
Associative laws
𝒑 ∨ (𝒒 ∧ 𝒓)
(𝒑 ∨ 𝒒) ∧ (𝒑 ∨ 𝒓)
𝒑 ∧ (𝒒 ∨ 𝒓) <=> (𝒑 ∧ 𝒒) ∨ (𝒑 ∧ 𝒓)
Distributive laws
~(𝒑 ∧ 𝒒 )<=> ~𝒑 ∨ ~𝒒
~(𝒑 ∨ 𝒒 ) <=> ~𝒑 ∧ ~𝒒
De Morgan’s laws
– a compound proposition that is ALWAYS
TRUE, regardless of the truth values of the propositions
that occur in it.
Tautology
a compound proposition that is ALWAYS
FALSE.
Contradiction
– neither a tautology nor a contradiction
Contingency
