#### Questions Discussed:

**Question 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. (N)

**Question 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? (N)

**Question 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? (N)

**Question 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. (N)

**Question 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. (P)

**Question 11.** Let R be the relation on set 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. (B)