# What is the law of transitivity?

## What is the law of transitivity?

Transitive law, in mathematics and logic, any statement of the form “If aRb and bRc, then aRc,” where “R” is a particular relation (e.g., “…is equal to…”), a, b, c are variables (terms that may be replaced with objects), and the result of replacing a, b, and c with objects is always a true sentence.

### What is transitivity in set theory?

From Wikipedia, the free encyclopedia. In set theory, a branch of mathematics, a set A is called transitive if either of the following equivalent conditions hold: whenever x ∈ A, and y ∈ x, then y ∈ A. whenever x ∈ A, and x is not an urelement, then x is a subset of A.

#### How do you know if a relationship is transitive?

Transitive: A relation R on a set A is called transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R, for all a, b, c ∈ A. If there is a path from one vertex to another, there is an edge from the vertex to another.

Where can I find the definition of transitivity?

Look up transitivity or transitive in Wiktionary, the free dictionary. Transitivity or transitive may refer to: Transitivity (grammar), a property of verbs that relates to whether a verb can take direct objects Transitive case, a grammatical case to mark arguments of a transitive verb

Which is the correct form of the transitive law?

Transitive law, in mathematics and logic, any statement of the form “If aRb and bRc, then aRc,” where “R” is a particular relation (e.g., “…is equal to…”), a, b, c are variables (terms that may be replaced with objects), and the result of replacing a, b, and c with objects is always a true sentence.

## Are there transitive laws for some relations but not for others?

There are transitive laws for some relations but not for others. A transitive relation is one that holds between a and c if it also holds between a and b and between b and c for any substitution of objects for a, b, and c. Thus, “…is equal to…” is such a relation, as is “…is greater than…” and “…is less than…”.

### Which is a property of a transitive verb?

Transitivity (grammar), a property of verbs that relates to whether a verb can take direct objects. Transitive verb, a verb which takes an object.