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?
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 point related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.
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.
Find the number of all onto functions from the set {1,2,3,… ,n) to itself.
Show that the relation R in the set R of real numbers, defined asR = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.
Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitivebut not symmetric.
Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R={(a,b) : Ia-bI 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}.
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer. A. R is reflexive and symmetric but not transitive. B. R is reflexive and transitive but not symmetric. C. R is symmetric and transitive but not reflexive. D. R is an equivalence relation.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N, a * a=a ∀ a * N. (ii) If * is a commutative binary operation on N, then a * (b * c)= (a * b)* a
Given an example of a relation. Which is(i) Symmetric but neither reflexive nor transitive.(ii) Transitive but neither reflexive nor symmetric.(iii) Reflexive and symmetric but not transitive.(iv) Reflexive and transitive but not symmetric.(v) Symmetric and transitive but not reflexive.
Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric or transitive
Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
Let A=N×N and * be the binary operation on A defined by (a, b)*(c, d)=(a+c,b+d) Show that * is commutative and associative. Find the identity element for * on A, if any.
Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related?
Show that each of the relation R in the set A = { x ∈ Z : 0 ≤ x ≤ 12}, given by I. R={(a,b):Ia-bI is a multiple of 4} II. R={(a,b):a=b}is an equivalence relation. Find the set of all elements related to 1 in each case.
Let \(f:\{1,3,4\}→\{1,2,5\}\) and g:{1,2,5}→{1,3} be given by f = {(1,2),(3,5),(4,1)} and g ={(1,3),(2,3),(5,1)}.Write down gof.