Show that the relation R on the set Z of all integers defined by (x, y) ∈ is divisible by 3 is an equivalence relation.
Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad(b + c) = bc(a + d). Show that R is an equivalence relation.
Show that the relation S in the set R of real numbers defined as S = {(a, b) : a, b ∈ R and a ≤ b³} is neither reflexive nor symmetric nor transitive.
If Z is the set of all integers and R is the relation on Z defined as R = {(a, b) : a, b ∈ Z and a – b is divisible by 5}. Prove that R is an equivalence relation.
Show that the relation R in the Set A = {1, 2, 3, 4,5} given by R = {(a, b) : |a – b| is divisible by 2} is an equivalence relation. Write all the equivalence classes of R.
Check whether the relation R in the set R of real numbers, defined by R = {(a, b) : 1 + ab > 0}, is reflexive, symmetric or transitive.
Let f : X -> Y be a function. Define a relation R on X given be R = {(a, b) : f(a) = f(b)}. Show that R is an equivalence relation ?
Find the particular solution of the differential equation : x ≠ 0. Given that y = 0, when
Three schools A, B and C organised a fete (mela) collecting funds for flood victims in which they sold hand-helds fans, mats and toys made from recycled material, the sale price of each being ₹ 25, ₹ 100 and ₹ 50 respectively. The following table shows the number of articles of each type sold :
To promote the making of toilets for women, as organisation tried to generate awareness through (i) house calls (ii) letters and (iii) announcements.
The cost for each mode per attempt is given below :
(i) ₹ 50 (ii) ₹ 20 (iii) ₹ 40
The number of attempts made in three villages X, Y and Z and given below :
Find the particular solution of the differential equation : 4x cosec x, (x ≠ 0), given, that y = 0,when
Find the equations of the tangent and the normal, to the curve 16x² + 9y² = 145 at the point where x₁ = 2 and y₁ > 0.
Find the particular solution of the differential equation given that y = 1, when x = 0.