Introduction of Relations and Functions

Let f: R → R be the function defined by f(x) = `1/(2 - cosx)` ∀ x ∈ R.Then, find the range of f

Number of relations that can be defined on the set A = {a, b, c, d} is ____________.

For the set A = {1, 2, 3}, define a relation R in the set A as follows: R = {(1, 1), (2, 2), (3, 3), (1, 3)}. Write the ordered pairs to be added to R to make it the smallest equivalence relation.

Solve the differential equation  `dy/dx = (x + y+2)/(2(x+y)-1)`

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}, then ______.

If A, B and C are the elements of Boolean algebra, simplify the expression (A’ + B’) (A + C’) + B’ (B + C). Draw the simplified circuit.

 Evaluate: `int_-6^3 |x+3|dx`

Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is ____________.