Answer the question number 14 by an expart — 'S a multiple of 41
relation. Find the set of elements related to 1 in each
ample of a relation. Which is
(i) Symmet/ic but neither reflexive nor transitive.
Give
Transitive but neither reflexive nor symmetnc.
Reflexive and syntmetric but not transitive.
(iv' Reflexive and transitive but not symmetric.
(v) Symmetric and uansitive but not reflexive.
II. 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
Q from the origin). is an equivalence relation. Further. show that the set of
all points related to a point (0. is the circle passing through P with origin as
centre.
12. Show that the relation R defined in the set A of all triangles as R = { (T, , T.) : T,
is similar to is equivalence relation. Consider three right angle triangles T,
with sides 3. 4, 5. T, with sides 5. 12. 13 and Ts with sides 6. 8, 10. Which
triangles among T, , T- and T. are related?
13. Show that the relation R defined in the set A of all polygons as R = ((P , P ) :
P, and P, have same number of sides l. is an equivalence relation. What is the
t of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
Let L be the set of all lines in XY plane and R be the relation in L defined as
R = I(L,. L,) : I-r is parallel to Show that R is an equivalence relation. Find
e set of all lines related to [he line y = 2x + 4.
