M1 Topic 2: Logical Equivalence Flashcards
P is logically equivalent to Q in symbols
P≡Q or P⟺Q
The propositions are said to be logically equivalent if their ______ are identical
truth tables
This is formed by interchanging the hypothesis and conclusion of the original statement
converse
The converse of p→q is
q→p
Conditional: “If 8 is an even number, then 8 is divisible by 2.”
Converse:
“If 8 is divisible by two, then 8 is an even number.”
Is the Converse of a given condition logically equivalent to the Condition?
No.
This is formed by negating the hypothesis and negating the conclusion of the original statement
inverse
The inverse of p→q is
￢p → ￢q
Conditional: “If 8 is an even number, then 8 is divisible by 2.”
Inverse:
“If 8 is not an even number, then 8 is not divisible by 2.”
Is the inverse of a given conditional statement logically equivalent to the conditional statement? Is the inverse logically equivalent to the CONVERSE of the conditional statement?
The inverse is logically equivalent to the converse of the conditional statement
This is formed by negating both the hypothesis and conclusion and then interchanging the negations (converse + inverse = ?)
contrapositive
The contrapositive of p →q is
￢q → ￢p
Is the contrapositive of a given conditional statement logically equivalent to the conditional statement?
Yes
A proposition is a ______ if its truth table contains only true values for every case
tautology
Two compound propositions, P and Q, are logically equivalent if P↔Q is a
tautology
