Question

Let A={0,1},B={2,3,4}and C={3,5}verity That Ax(BUC)=(AxB) U (AxC)

Answer 1

Answer:

Step-by-step explanation:

Given:

A={0,1}  b={2,3,4}  c={3,5}

Taking LHS,

Ax(BUC)

Here

BUC={2,3,4,5}  

Now

Ax(BUC)

{0,1}x{2,3,4,5}

=[(0,2),(0,3),(0,4),(0,4),(1,2),(1,3),(1,4),(1,5)]=LHS

Taking RHS

(AxB)u(AxC)

Here AxB={0,1}x{2,3,4}

               =[(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)]

Here AxC={0,1}x{3,5}=[(0,3),(0,5),(1,3),(1,5)]

Now (AxB)U(AxC)=[(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)]U[(0,3),(0,5),(1,3),(1,5)]

                             =[(0,2),(0,3),(0,4),(0,4),(1,2),(1,3),(1,4),(1,5)]=RHS

Here LHS=RHS

Hence, Proved

Ax(BUC)=(AxB)U(AxC)

I hope it helps You

Answer 2

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 \}}A×B={(x,y):x∈Aandy∈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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