9. PYQ - Prove the following

Let \(A =\) The set of all natural numbers less than \(3\), \(B =\) The set of all prime numbers less than \(9\), \(C =\) The set of even prime numbers. Demonstrate that \(A \times (B - C) = (A \times B) - (A \times C)\)

 

Answer:

 

To prove:

 

\(A \times (B - C) = (A \times B) - (A \times C)\)

 

Explanation:

 

\(B - C =\)

 

\(A \times (B - C) =\)

 

\(A \times B =\)

 

\(A \times C =\)

 

\((A \times B) - (A \times C) =\)

 

Therefore, \(A \times (B - C) = (A \times B) - (A \times C)\)