Question

if A= (1,2,3), and B = (4,5) then number of relation A to B is​

Answer 1

Step-by-step explanation:

In Set A n(A)=3

In Set B n(B)=2

relation AtoB

2^3×2

2^6

64 is the answer

Answer 2

SOLUTION

GIVEN

A = { 1 , 2 , 3 } and B = { 4 , 5 }

TO DETERMINE

The number of relation from A to B

CONCEPT TO BE IMPLEMENTED

SET :

A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

SUBSET :

A set S is said to be a subset of T if every element of S is an element of T

CARTESIAN PRODUCT :

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

RELATION :

Let A and B are two non empty sets. Then a Relation R from A to B is a Subset of A × B

EVALUATION

Here the given sets are

A = { 1 , 2 , 3 }

B = { 4 , 5 }

Now n(A) = 3 , n(B) = 2

We know that a Relation R from A to B is a Subset of A × B

Hence the number of relation from A to B

= The number of Subset of A × B

$\sf = {2}^{(3 \times 2)}$

$\sf = {2}^{6}$

$\sf = 64$

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