- its
logically equivalent contrapositive, and an ****ociated
proof method known as
proof by contraposition. The
contrapositive of a
statement has its antecedent...
- In logic, the
contrapositive of a
conditional statement is
formed by
negating both
terms and
reversing the
direction of inference. More specifically, the...
-
application of the
general truth that if a
statement is true, then so is its
contrapositive. The form
shows that
inference from P
implies Q to the
negation of Q...
- f(x2). (Equivalently, f(x1) = f(x2)
implies x1 = x2 in the
equivalent contrapositive statement.) In
other words,
every element of the function's codomain...
- ¬P→¬Q{\displaystyle \neg P\rightarrow \neg Q}.
Since an
inverse is the
contrapositive of the converse,
inverse and
converse are
logically equivalent to each...
- Name
Statement Contrapositive /
Obverted Contrapositive Contrapositive per
accidens /
Obverted Contrapositive per
accidens /
Condition of
Validity A All...
-
either the
original subject, or its contradictory,
resulting in two
contrapositives which are the
obverts of one
another in the "A", "O", and "E" type...
- make the
immediate inference that "All non-P are non-S"
which is the
contrapositive of the
given statement.
Given a type O statement, "Some S are not P...
- the
integral test for convergence. The test is
typically proven in
contrapositive form: If ∑n=1∞an{\displaystyle \sum _{n=1}^{\infty }a_{n}} converges...
- A^{\complement }.} (this
follows from the
equivalence of a
conditional with its
contrapositive).
Involution or
double complement law: ( A ∁ ) ∁ = A . {\displaystyle...
