ashish kumar

Ch1. Relations and Functions (Part - 1)

In this self study course, you will learn Empty Relations, Universal Relations, Trivial Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, Equivalence Classes. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

Total Video Duration  6 hr 11 min 22 sec
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Assignment – 2

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Question – 2

2. Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

 06:18

Question – 3

3. Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a – b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

 16:09

Question – 4

4. Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

 02:23

Question – 5

5. Show that each of the relation R in the set \displaystyle A=\{x\in Z:0\le x\le 12\}, given by
A. R = {(a, b) : |a – b| is a multiple of 4}
B. R = {(a, b) : a = b}
is an equivalence relation. Find the set of all elements related to 1 in each case.

 22:11

Question – 6

6. Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.

 13:22

Question – 7

7. Show that the relation R defined in the set A of all triangles as R=\{({{T}_{1}},\,{{T}_{2}}):\,{{T}_{{1\,}}}\,\text{is}\,\text{similar}\,\text{to}\,{{T}_{2}}\} is equivalence relation. Consider three right angle triangles {{T}_{1}} with sides 3, 4, 5, {{T}_{2}} with sides 5, 12, 13 and {{T}_{3}} with sides 6, 8, 10. Which triangles among {{T}_{1}},\,\,{{T}_{2}}\,\,\text{and}\,\,{{T}_{3}} are related?

 06:42

Question – 10

10. Let A = {0, 1, 2, 3, 4} and define a relation R on A as follows:
R = {(0, 0), (0, 4), (1, 1), (1, 3), (2, 2), (3, 1), (3, 3), (4, 0), (4, 4)}.
As R is an equivalence relation on A. Find the distinct equivalence classes of R.

 05:02

Question – 11

11. Let R be the relation on set \displaystyle A=\{x\in Z:0\le x\le 10\} given by R = {(a, b) : ( a-b) is divisible by 4}. Show that R is an equivalence relation. Also, write all elements related to 4.

 13:17

Question – 8

8. Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

 12:13

Question – 9

9. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2 }. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

 15:51