Question

If A= {x:x €n, x<7}, B={x:x is prime , x<8}and C={ x:x€N is an odd no. and x< 10}. verify that A intersection ( B union B)=(A intersection B) union(A intersection C)​

Answer 1

$\bf\huge\underline{\underline{ Answer :- }}$

• A = { 1 , 2 , 3 , 4 , 5 , 6 }

• B = { 2 , 3 , 5 , 7 }

• C = { 1 , 3 , 5 , 7 , 9}

$\rule{10cm}{0.0005cm}$

• A $\cap$ (B $\cup$ C ) = (A $\cap$ B ) $\cup$ ( A $\cap$ C )

LHS

• A $\cap$ (B $\cup$ C )

• $\red{\implies}$ {1 ,2 , 3 , 4 , 5 , 6 } $\cap$( { 2 , 3 , 5 , 7 } $\cup$ { 1 , 3 , 5 , 7 , 9 } )

• $\red{\implies}$ { 1 , 2 , 3 , 5 }

RHS

• (A $\cap$ B ) $\cup$ ( A $\cap$ C )

• $\red{\implies}$ ( { 2 , 3 , 5 }) $\cup$( { 1 , 3 , 5 } )

• $\red{\implies}$ { 1 , 2 , 3 , 5 }

$\rule{10cm}{0.05cm}$

LHS = RHS

ie ,

A $\cap$ (B $\cup$ C ) = (A $\cap$ B ) $\cup$ ( A $\cap$ C )

Answer 2

Answer:

Answer:−

A = { 1 , 2 , 3 , 4 , 5 , 6 }

B = { 2 , 3 , 5 , 7 }

C = { 1 , 3 , 5 , 7 , 9}

\rule{10cm}{0.0005cm}

A \cap∩ (B \cup∪ C ) = (A \cap∩ B ) \cup∪ ( A \cap∩ C )

LHS

A \cap∩ (B \cup∪ C )

\red{\implies}⟹ {1 ,2 , 3 , 4 , 5 , 6 } \cap∩ ( { 2 , 3 , 5 , 7 } \cup∪ { 1 , 3 , 5 , 7 , 9 } )

\red{\implies}⟹ { 1 , 2 , 3 , 5 }

RHS

(A \cap∩ B ) \cup∪ ( A \cap∩ C )

\red{\implies}⟹ ( { 2 , 3 , 5 }) \cup∪ ( { 1 , 3 , 5 } )

\red{\implies}⟹ { 1 , 2 , 3 , 5 }

\rule{10cm}{0.05cm}

LHS = RHS

ie ,

A \cap∩ (B \cup∪ C ) = (A \cap∩ B ) \cup∪ ( A \cap∩ C )

Step-by-step explanation:

I hope you understood