The importance of Relations

All arguments depend upon the relationship of terms. The awareness of the types of relations helps us resolve many of the issues in interpretation.

Relation between two terms is Didadic or Binary Relation. Example: Cat sat on mat, the terms of relation are Cat and mat. Relation between three terms is Triadic Relation. Example: Johnny gives milk to the baby, the terms of relation are Johnny, milk and baby.  Relation between Four terms is Tetradic Relation. Example: He gave a gift to me on my birthday, the terms are He, gift, me and birthday. Relation between five terms is Pentadic relation. Example: He gave gift to me and my mother on my birthday, the terms are He, gift, me,mother and birthday. Relation between more than five terms is Polyadic relation.

Relations are classfified as (i) Symmetrical, Assymetrical and Non-Symmetrical, (ii) Transitive, Intrasnitive and Non-Transitive, (iii) Totally Reflexive, Irreflexive and Non-Reflexive.

Symmetrical Relation is a relation where if A has relation to B, then B should have relation to A. For example: If A is married to B, then B is also married to A. Symbollicaly represented as follows: (x) (y) (Rxy implies Ryx)/ (Mab implies Mba)

Asymmetrical Relation is a relation where if A has relation to B but B does not have the same relation to A. Example: Kolkata is to east of Mumbai but Mumbai is not to east of Kolkata. Symbolically represented as, (x) (y) (Rxy implies NOT Ryx)/ (Ekm implies NOT Emk)

Non-Symmetrical relations are those where is A is related to B then B may or may not be related to A. Example: A is sister of B but B may or may not be sister of A. It cannot be symobolized. It can be Symmetrical or Assymetrical.

Transitive relation is such that if A has relation to B and B has relation to C then A must have same relation to C. Example: Japan is east of Kolkata and Kolkata is east of Mumbai therefore Japan is east of Mumbai. Symbolically represented as (x) (y) ( Rxy. Ryz) implies Rxz/ (Ejk.Ekm) implies Ejm

Intransitive relation is such that if A has relation to B and B has relation to C then A cannot have same relation to C. Example: John is father of Tom and Tom is father of Leo then John is not father of Leo. Symbolically represented as (x) (y) (Rxy.Ryz) implies Not Rxz/ (Fjt.Ftl) implies NOT Fjl

Non-Transitive relation is such that if A has relation to B and B has relation to C then A may or may not have relation to C. Example: If A loves B and B loves C then A may or may not love C. Example: Granny loves her Daughter and Daughter loves her Brother but Granny may or may not love Daughters Brother. No symbolization is possible.

Totally Reflexive is a relation which the term has with itself. Example: Dhanashree is identical with Dhanashree. Symbolically represented as (x) Rxx/ Idd

Irreflexive relation is when nothing has to itself. Example: I cant be to east of myself. Symbolically represented as (x) Rx-x/ Ei-i

Non-Reflexive are relations which are neither Reflexive nor Irreflexive. Example: I love myself. I may not love myself. No symbolization.