Q1 of 50 Page 28

State whether each of the following arrow diagrams define a function or not. Justify your answer.

If P and Q are two relation then the two most important conditions for the relation to be treated as a function are as follows,


● Each element of P must have a unique image in Q.


● Each element of P has to be mapped with only one element in Q


If either of the above conditions is not satisfied, then the relation can’t be consider as a function.



(i) The figure shows mapping from P to Q, the element "C" in P does not have any image in Q. Since, the above given relation does not meet the conditions for relation and functions mentioned above so it is not a function.



(ii) In the above mapping from L to m, each element of L has an image in M and the number of image for each element is one. Since, the above given relation satisfies all the conditions of relation and function mentioned above, so it is a function.


More from this chapter

All 50 →
8

In a school of 4000 students, 2000 know French, 3000 know Tamil and 500 know Hindi, 1500 know French and Tamil, 300 know French and Hindi, 200 know Tamil and Hindi and 50 know all the three languages.

(i) How many do not know any of the three languages?


(ii) How many know at least one language?


(iii) How many know only two languages?

 9

In a village of 120 families, 93 families use firewood for cooking, 63 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 24 families use kerosene and cooking gas, 27 families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas.

 2

For the given function F = { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) }, write the domain and range.

 3

Let A = { 10, 11, 12, 13, 14 }; B = { 0, 1, 2, 3, 5 } and fi : A → B , i = 1,2,3.

State the type of function for the following (give reason):


(i) f1 = { (10, 1), (11, 2), (12, 3), (13, 5), (14, 3) }


(ii) f2 = { (10, 1), (11, 1), (12, 1), (13, 1), (14, 1) }


(iii) f3 = { (10, 0), (11, 1), (12, 2), (13, 3), (14, 5) }