A relation between two persons is defined as follows: a R b 'if a and b born in different months

step 1 students in this question we are given two persons a and b okay and we are given that a will hav

A relation between two persons is defined as follows: a R b...

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Key Concepts

Relation

A relation is a connection or association between elements of a set or between elements of different sets. It defines how elements can be paired based on a specific criterion, allowing comparisons and classification of properties among these elements.

Reflexivity

Reflexivity is a property of a relation where every element is related to itself. In other words, a relation R on a set is reflexive if for every element a in the set, the pair (a, a) is included in R.

Symmetry

Symmetry in a relation means that if one element is related to a second element, then the second element is also related to the first. Formally, a relation R is symmetric if for all elements a and b, whenever (a, b) is in R, then (b, a) is also in R.

Transitivity

Transitivity is a property of a relation where the relation can be 'transferred' along a chain of elements. Specifically, a relation R is transitive if whenever an element a is related to b and b is related to c, then a must also be related to c.

Equivalence Relation

An equivalence relation is a special type of relation that is reflexive, symmetric, and transitive. These properties together partition a set into equivalence classes, where each element of the set belongs to one class that groups together elements sharing a common relation.

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