Question

if n(A)=5,n(B)=6 , n(C)=7 n A intersection C=4 then the number of elements in AXBXC intersection CXBXA​

Answer 1

SOLUTION

GIVEN

n(A) = 5 , n(B) = 6 , n(C) = 7 , n(A ∩ C) = 4

TO DETERMINE

The number of elements in

( A × B × C ) ∩ ( C × B × A )

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

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

EVALUATION

Here it is given that

n(A) = 5 , n(B) = 6 , n(C) = 7 , n(A ∩ C) = 4

Now the number of elements in ( A × B × C ) ∩ ( C × B × A )

= n [ ( A × B × C ) ∩ ( C × B × A ) ]

= n(A ∩ C) × n(B) × n(A ∩ C)

= 4 × 6 × 4

= 96

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