Relations

We approach the concept of relations in different aspects using real life sense, Cryptography and Geometry through Cartesian product of sets. In our day to day life very often we come across questions like, “ How is he related to you?” . Some probable answers are, (i) He is my father. (ii) He is my teacher.

(iii) He is not related to me. From this we see that the word relation connects a person with another person. Extending this idea, in mathematics we consider relations as one which connects mathematical objects. Examples, (i) A number m is related to a number n if m divides n in N .

(ii) A real number x is related to a real number y if x ≤ y . (iii) A point p is related to a line L if p lies on L . (iv) A student X is related to a school S if X is a student of S . Illustration .

(Cryptography) For centuries, people have used ciphers or codes, to keep confi- dential information secure. Effective ciphers are essential to the military, to financial institutions and to computer programmers. The study of the techniques used in creating coding and decoding these ciphers is called cryptography.