all physical research. – BERTHELOT v . Introduction Much of mathematics is about finding a pattern – a recognisable link between quantities that change. In our daily life, we come across many patterns that characterise relations such as brother and sister, father and son, teacher and student.
In mathematics also, we come across many relations such as number m is less than number n , line l is parallel to line m , set A is a subset of set B. In all these, we notice that a relation involves pairs of objects in certain order. In this Chapter, we will learn how to link pairs of objects from two sets and then introduce relations between the two objects in the pair. Finally, we will learn about special relations which will qualify to be functions.
The concept of function is very important in mathematics since it captures the idea of a mathematically precise correspondence between one quantity with the other. . Cartesian Products of Sets Suppose A is a set of colours and B is a set of objects, i.e., A = {red, blue}and B = { b , c , s }, where b , c and s represent a particular bag, coat and shirt, respectively. How many pairs of coloured objects can be made from these two sets?
Proceeding in a very orderly manner, we can see that there will be distinct pairs as given below: (red, b ), (red, c ), (red, s ), (blue, b ), (blue, c ), (blue, s ). Thus, we get distinct objects (Fig . ). Let us recall from our earlier classes that an ordered pair of elements taken from any two sets P and Q is a pair of elements written in small Fig .