Test 1

        

CHAPTER 1 - SETS, RELATIONS AND FUNCTIONS

SET 1

1. Find the number of subsets of  if  (EG 1.1)
2. If  and  find the number of sets  such that  (Eg. 1.4)
3. If  and  find  (EG 1.7)
4. If  denotes the power set of A, then find (Eg. 1.9)If  and  find  (Eg. 1.8)
5. Write the following in roster form. and  is a prime (EX 1.1 - 1)

SET 2

6. If  and  then find  (EX. 1.1 - 6)
7. If and then find  (EX 1.1 - 7)
8. For a set contains  elements and two of its elements are  and  Find the elements of  (EX 1.1 - 8)
9. Check whether the following functions are one-to-one and onto. defined by          defined by  (EG 1.14)
10. Check the following functions for one-to-oneness and ontoness.  defined by     defined by  (EG 1.15)

SET 3

11. Check whether the following for one-to-oneness and ontoness.   defined by           defined by  (EG 1.16)
12. If  is given by  then find  so that  is onto. (EG 1.19)
13. Find the domain of  (EG 1.22)        
14. Let  and  Find  and  (EG 1.25) 
15. Let  and  Find  Can you find  (EG 1.26) 
16. Let  and  be the two functions from  to  defined by  and  Find  and  (EG 1.27)

SET 4

17. Find the domain of  (EX 1.3 - 6)
18. The weight of the muscles of a man is a function of his body weight  and can be expressed as  Determine the domain of this function. (EX 1.3 - 13)
19. For the curve  given in the Figure, draw  with the same scale. (EX 1.4 - 1)
20. Graph the functions  and  on the same coordinate plane. Find and graph it on the plane as well. Explain your results. (EX. 1.4 - 3)
21. From the curve draw  (EX. 1.4 - 8)

                

SET 1

1. In a survey of  persons in a town, it was found that  of the persons know Language   know Language  know Language  know Languages  and  know Languages  and  and  know Languages  and  If  of the persons know all the three Languages, find the number of persons who knows only Language . (EG 1.2)
2. If  and  are two sets so that  and if  then find  (EG 1.5)
3. Two sets have  and  elements. If the total number of subsets of the first set is 112 more than that of the second set, find the values of  and  (EG 1.6)
4. Check the relation  defined on the set  for the three basic relations. (EG 1.10)
5.  Discuss the following relations for reflexivity, symmetricity and transitivity:    On the set of natural numbers the relation R defined by if  (EX 1.2 - 1)
6. On the set of natural numbers let  be the relation defined by  if  Write down the relation by listing all the pairs. Check whether it is   reflexive  symmetric  transitive  equivalence (EX 1.2 - 5)

SET 2

7. On the set of natural numbers let  be the relation defined by  if  Write down the relation by listing all the pairs. Check whether it is  reflexive  symmetric  transitive  equivalence (EX 1.2 - 7)
8. Let  What is the equivalence relation of smallest cardinality on  What is the equivalence relation of largest cardinality on  (EX 1.2 - 8)
9. If  is defined by  verify whether  is one-to-one or not. (EG 1.17)
10. If  is defined as  find the pre-images of  and  (EG 1.18)
11. Find the largest possible domain for the real valued function  defined by  (EG 1.21)
12. Find the range of the function  (EG 1.23)

SET 3

13. Find the largest possible domain for the real valued function given by  (EG 1.24)
14. Let  be defined as  and  Find  (EG 1.29)
15. Write the values of  at   (EX 1.3 - 2)
16. Write the values of  at   (EX 1.3 - 3)
17. Find the range of the function  (EX 1.3 - 8)
18. Show that the relation  is a function for a suitable domain. Find the domain and the range of the function. (EX 1.3 - 9)

By Samy Sir, Ph:7639147727Page