LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RELATION & MAPPING - MAPPING

__MAPPING__

**Let, A &
B be two non-empty sets, Then a relation which associates each member of A with
exactly one member of B is called a Mapping from set A to set B. The unique
element b of B that is linked to an element a of set A is called the image of a in B. A mapping is also known as a function. **

**Let A = {1,
2, 3, 4, 5} and B = {a, b, c, d, e}.
Consider the following relations from set A to set B**

**1) R = {(1, a), (2, c), (3, b), (4, d), (5, e)}**

**2) R = {(1, a), (3, d), (3, e), (4, c), (5, c)}**

**3) R = {(1, a), (2, a), (3, b), (3, c), (4, c),
(5, d), (5, e)}**

**4) R = {(1, b), (2, b), (2, c), (3, d), (4, d),
(5, e)} **

**5) R = {(1, a), (2, b), (3, c), (4, d), (5, e)}**

**1) R = {(1, a), (2, c), (3, b), (4, d), (5, e)}**

**In (1) each member
of set A is associated with only one member of B, so, relation (1) is a mapping
of function.**

**2) R = {(1, a), (3, d), (3, e), (4, c), (5, c)}**

**In(2) the
member ā2ā of set A is not associated with any member of set B. so, relation
(2) is not a mapping of function.**

**3) R = {(1, a), (2, a), (3, b), (3, c), (4, c),
(5, d), (5, e)}**

**In (3) each
member of set A is associated with member of set B. Thus even through two
members of set A, 1 and 2 are associated with the same member of set B. The
single member 3 of set A, is associated with two members b & c of set B.
The two members 3 & 4 of set A, are associated with the same member ācā of
set B. The single member 5 of set A is associated with two members d & e of
set B, the relation (3) is not a mapping or function**

**4) R = {(1, b), (2, b), (2, c), (3, d), (4, d),
(5, e)}**

**In (4) each
member of set A is associated with member of set B. Thus, even through two
members 1 & 2 of set A, are associated with the member b of set B. the
member 2 of set A is associated with two members b & c of set B. The two
members 3 & 4 of set A are associated with member d of set B. the member 5
of set A is associated with member e of set B, but no member of set A is
associated with the member a of set B. The relation (4) is not a mapping or
function.**

**5) R = {(1, a), (2, b), (3, c), (4, d), (5, e)}**

**In (5) each
member of set A is associated with each member of set B. here each and every
single member of set A associated with each and every single member of set B.
The relation (5) is a mapping or function.**