- its
logically equivalent contrapositive, and an ****ociated
proof method known as § Proof by
contrapositive. The
contrapositive of a
statement has its antecedent...
-
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...
- {\displaystyle \neg P\rightarrow \neg Q} .
Since an
inverse is the
contrapositive of the converse,
inverse and
converse are
logically equivalent to each...
- a\neq b,} then f ( a ) ≠ f ( b ) {\displaystyle f(a)\neq f(b)} in the
contrapositive statement. Symbolically, ∀ a , b ∈ X , f ( a ) = f ( b ) ⇒ a = b , {\displaystyle...
- 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...
- A^{\complement }.} (this
follows from the
equivalence of a
conditional with its
contrapositive).
Involution or
double complement law: ( A ∁ ) ∁ = A . {\displaystyle...
- Name
Statement Contrapositive /
Obverted Contrapositive Contrapositive per
accidens /
Obverted Contrapositive per
accidens /
Condition of
Validity A All...
- then "this
person does not live in San Diego" (non-P). This is the
contrapositive of the
first statement, and it must be true if and only if the original...
- conjecture, the idea that an
absence of
detectable Von
Neumann probes is
contrapositive evidence that no
intelligent life
exists outside of the Sun's Solar...
- the
integral test for convergence. The test is
typically proven in
contrapositive form: If ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} converges...
