1. opposite, reverse, contrary, other side of the coin, obverse, antithesis If that is true, the converse is equally so.

conversely Add to list Share. The word conversely is an adverb that means “the opposite” or “on the other hand.” It is often used to introduce an idea that is different from one stated before. You say the photo is a fake. Conversely, the photographer claims it’s real.

Conversely in a Sentence 🔉

1. The trip wasn’t all good, and conversely, it wasn’t all bad.
2. Conversely, if you don’t hug your children often, they may grow up to become unaffectionate people.
3. While my husband is a Republican voter, I, conversely, am a member of the Democratic Party.

What is another word for conversely?

Opposite of in a contrary manner. likewise. equally. similarly. correspondingly.

Definition of Inverse? In mathematics, the word inverse refers to the opposite of another operation.

: a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them “if not-B then not-A ” is the contrapositive of “if A then B “

As nouns the difference between contrapositive and contraposition. is that contrapositive is (logic) the inverse of the converse of a given proposition while contraposition is (logic) the statement of the form “if not q then not p”, given the statement “if p then q”.

In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as proof by contraposition. The contrapositive of a statement has its antecedent and consequent inverted and flipped.

More specifically, the contrapositive of the statement “if A, then B” is “if not B, then not A.” A statement and its contrapositive are logically equivalent, in the sense that if the statement is true, then its contrapositive is true and vice versa.

And our contrapositive statement would be: “If the grass is NOT wet, then it is NOT raining.” For example, consider the statement, “If it is raining, then the grass is wet” to be TRUE. Then you can assume that the contrapositive statement, “If the grass is NOT wet, then it is NOT raining” is also TRUE.

The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true. A pattern of reaoning is a true assumption if it always lead to a true conclusion.

So, in proof by contraposition we assume that is false and then show that is false. It differs from proof by contradiction in the sense that, in proof by contradiction we assume to be false and to true and show that such an assumption leads to something which is known to be false .

Direct Proof

1. You prove the implication p –> q by assuming p is true and using your background knowledge and the rules of logic to prove q is true.
2. The assumption “p is true” is the first link in a logical chain of statements, each implying its successor, that ends in “q is true”.

Contrapositive: The contrapositive of a conditional statement of the form “If p then q” is “If ~q then ~p”. Symbolically, the contrapositive of p q is ~q ~p. A conditional statement is logically equivalent to its contrapositive.

The inverse of p → q is ∼ p →∼ q. A conditional statement and its converse are NOT logically equivalent.

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S.

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form. Two line segments are congruent if and only if they are of equal length. A biconditional is true if and only if both the conditionals are true.

Definition: A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow . The biconditional p q represents “p if and only if q,” where p is a hypothesis and q is a conclusion.

A disjunction is a compound statement formed by combining two statements using the word or . Example : Consider the following statements. p:25×4=100. q : A trapezoid has two pairs of opposite sides parallel.

The biconditional statement “−1 ≤ x ≤ 1 if and only if x2 ≤ 1” can be thought of as p ⇔ q with p being the statement “−1 ≤ x ≤ 1” and q being the statement “x2 ≤ 1”. Thus, we we will prove the following two conditional statements: p ⇒ q: If −1 ≤ x ≤ 1, then x2 ≤ 1. q ⇒ p: If x2 ≤ 1, then −1 ≤ x ≤ 1.

In logic and related fields such as mathematics and philosophy, “if and only if” (shortened as “iff”) is a biconditional logical connective between statements, where either both statements are true or both are false.

The converse is logically equivalent to the inverse of the original conditional statement.

From Wikipedia, the free encyclopedia. In logic and mathematics, statements and are said to be logically equivalent if they are provable from each other under a set of axioms, or have the same truth value in every model.

Two statement forms are logically equivalent if, and only if, their resulting truth tables are identical for each variation of statement variables. p q and q p have the same truth values, so they are logically equivalent.

The inverse of a conditional statement is when both the hypothesis and conclusion are negated; the “If” part or p is negated and the “then” part or q is negated. In Geometry the conditional statement is referred to as p → q.