The number of constant functions from a set containing m elements to a set containing n elements is

The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is

Let A and B be subsets of the universal set N, the set of natural numbers. Then A^'∪[(A⋂B)∪B^'] is

If n(A) = 2 and n(B ∪ C) = 3, then n[(A \(\times\) B) ∪ (A \(\times\) C)] is

If two sets A and B have 17 elements in common, then the number of elements common to the set A \(\times\)B and B \(\times\)A is

State whether the following sets are finite or infinite.
{x \(\in \) N : x is an odd prime number}

State whether the following sets are finite or infinite.
{x \(\in \) Z : x is even and less than 10}

Discuss the following relations for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the members of a family. The relation R defined by "aRb if a is not a sister of b".

Discuss the following relations for reflexivity, symmetricity and transitivity :
Let A be the set consisting of all the female members of a family. The relation R defined by "aRb if a is not a sister of b".

Show that the relation R on R defined as R = {(a, b) : a ≤ b} is reflexive and transitive but not symmetric.

If n(A\(\cap\)B) = 3 and n(A\(\cup\)B) = 10 then find n(P(A \(\Delta \) B))

For a set A, A\(\times\)A contains 16 elements and two of its elements are (1, 3) and (0, 2). Find the elements of A.

Which of the following sets are finite and which are infinite?
{x ∈ R: 0 < x < 1}

If R is the set of all real numbers, what do the cartesian products R \(\times\) Rand R \(\times\)R \(\times\)R represent?

Find the domain and range of the function f(x) = \(\frac { 1 }{ \sqrt { x-5 } } \).

A simple cipher takes a number and codes it, using the function f(x) = 3x - 4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x(by drawing the lines)

Show that the relation R on the set R of all real numbers defined as R = {(a, b): a < b²} is neither reflexive, nor symmetric nor transitive.

Let A = R - [2] and B = R - [1]. If f : A ⟶ B is a mapping defined by \(f(x)={x-1\over x-2}\) Show that f is one-one and onto.

A relation R is defined on the set z of integers as follows:
(x, Y) ∈ R ⇔ x² + y² = 25. Express R and R^-1 as the set of ordered pairs and hence find their respective domains.