Question

A = {0,1), B = (2,3,4} மற்றும் C = (3, 5 )A x (BUC) = (AXB) U (AXC) என்ற

சமன்பாட்டினை

Answer 1

SOLUTION

GIVEN

A = { 0 , 1 } , B = { 2 , 3 , 4 } , C = { 3 , 5 }

TO VERIFY

A × ( B ∪ C ) = ( A × B ) ∪ ( A × C )

CONCEPT TO BE IMPLEMENTED

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

A = { 0 , 1 } , B = { 2 , 3 , 4 } , C = { 3 , 5 }

We have to verify

A × ( B ∪ C ) = ( A × B ) ∪ ( A × C )

Now

B ∪ C = { 2 , 3 , 4 , 5 }

∴ LHS

= A × ( B ∪ C )

= { (0,2) , (0,3) , (0,4) , (0,5) , (1,2) , (1,3) , (1,4) , (1,5) }

Again

( A × B )

= { (0,2) , (0,3) , (0,4) , (1,2) , (1,3) , (1,4) }

( A × C )

= { (0,3) , (0,5) , (1,2) , (1,3) , (1,4) , (1,5) }

∴ RHS

= ( A × B ) ∪ ( A × C )

= { (0,2) , (0,3) , (0,4) , (0,5) , (1,2) , (1,3) , (1,4) , (1,5) }

∴ LHS = RHS

Hence verified

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