Question

The function f:N to R is defined by f(n)=2^n. The range of the function is:

options:
a)the set of all even positive integers.
b)N
c)R
d)a subset of set of all even positive integers.​

Answer 1

A relation R from a non-empty set A to a non empty set B is a subset of the Cartesian
product A × B. The set of all first elements of the ordered pairs in a relation R from a
set A to a set B is called the domain of the relation R. The set of all second elements in
a relation R from a set A to a set B is called the range of the relation R. The whole set
B is called the codomain of the relation R. Note that range is always a subset of
codomain.
1.1.2 Types of Relations
A relation R in a set A is subset of A × A. Thus empty set φ and A × A are two extreme
relations.
(i) A relation R in a set A is called empty relation, if no element of A is related to any
element of A, i.e., R = φ ⊂ A × A.
(ii) A relation R in a set A is called universal relation, if each element of A is related
to every element of A, i.e., R = A × A.
(iii) A relation R in A is said to be reflexive if aRa for all a∈A, R is symmetric if
aRb ⇒ bRa, ∀ a, b ∈ A and it is said to be transitive if aRb and bRc ⇒ aRc
∀ a, b, c ∈ A. Any relation which is reflexive, symmetric and transitive is called
an equivalence relation.
Note: An important property of an equivalence relation is that it divides the set
into pairwise disjoint subsets called equivalent classes whose collection is called
a partition of the set. Note that the union of all equivalence classes gives
the whole set.
1.1.3 Types of Functions
(i) A function f : X → Y is defined to be one-one (or injective), if the images of
distinct elements of X under f are distinct, i.e.,
x1
, x2 ∈ X, f (x1) = f (x2) ⇒ x1
= x2
. (ii) A function f : X→ Y is said to be onto (or surjective), if every element of Y is the
image of some element of X under f, i.e., for every y ∈ Y there exists an element
x ∈ X such that f (x) = y.

Answer 2

hey mate here ur answer













option D) a subset of set of all even positive integers.....





I HOPE IT'S WILL HELP YOU




PLEASE MARK ME AS BRIAN LIST