## 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.