In the previous post we have discussed about Define one to one correspondence and In today's session we are going to discuss about function and relation.
Function and relation are two different concepts of mathematics. A relation is resembles a function only if it is one – one & onto. Therefore, we can say that all functions are relations but not all relations can be functions. In the Cartesian system we represent the 1st value of ordered pairs as the x – coordinate and the 2nd value as the y – coordinate. So, we can define a relation a usual set of orderly pairs and the mapping is not necessarily be one – one & onto.
Suppose we have two sets A = 2, 4, 5, 6, 8, 10 and B = 4, 16, 8, 10, 12. The mapping is done from set A to set B such that the elements in set B consist of multiples in set A. Element 4 of set B has multiples as 2 & 4 in set A. Similarly, for 16 we have 2, 4 & 8, for 8 we have 2, 4 & 8, for 10 we have 2, 5 & 10 and for 12 we have 2, 4 and 6. Thus this mapping is one to many mapping and thus this relation does not represent a function. Thus the ordered pairs we form are: (2, 4), (4, 4), (2, 16), (4, 16), (8, 16), (2, 8), (4, 8), (8, 8), (2, 10), (5, 10), (10, 10), (2, 12), (6, 12) and (4, 14).
To define a functionhttp://en.wikipedia.org/wiki/Function_(mathematics) we must have unique output for every input i.e. one value in range for every value in domain and also all the values of domain and range must be covered. For instance, we have pairs like: (1, 2), (4, 8), (2, 4), (3, 6) and (5, 10).
Next we study about how to find the surface area of a cylinder. For this we have a general formula that is given as follows: 2 pi a2 + 2 pi a l. Where, a and l are the radius and height of the cylinder. These concepts are detailed in the icse syllabus 2013.
Function and relation are two different concepts of mathematics. A relation is resembles a function only if it is one – one & onto. Therefore, we can say that all functions are relations but not all relations can be functions. In the Cartesian system we represent the 1st value of ordered pairs as the x – coordinate and the 2nd value as the y – coordinate. So, we can define a relation a usual set of orderly pairs and the mapping is not necessarily be one – one & onto.
Suppose we have two sets A = 2, 4, 5, 6, 8, 10 and B = 4, 16, 8, 10, 12. The mapping is done from set A to set B such that the elements in set B consist of multiples in set A. Element 4 of set B has multiples as 2 & 4 in set A. Similarly, for 16 we have 2, 4 & 8, for 8 we have 2, 4 & 8, for 10 we have 2, 5 & 10 and for 12 we have 2, 4 and 6. Thus this mapping is one to many mapping and thus this relation does not represent a function. Thus the ordered pairs we form are: (2, 4), (4, 4), (2, 16), (4, 16), (8, 16), (2, 8), (4, 8), (8, 8), (2, 10), (5, 10), (10, 10), (2, 12), (6, 12) and (4, 14).
To define a functionhttp://en.wikipedia.org/wiki/Function_(mathematics) we must have unique output for every input i.e. one value in range for every value in domain and also all the values of domain and range must be covered. For instance, we have pairs like: (1, 2), (4, 8), (2, 4), (3, 6) and (5, 10).
Next we study about how to find the surface area of a cylinder. For this we have a general formula that is given as follows: 2 pi a2 + 2 pi a l. Where, a and l are the radius and height of the cylinder. These concepts are detailed in the icse syllabus 2013.
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