17. Five marks exercise problems VIII

Let \(A =\) The set of all natural numbers less than \(8\), \(B =\) The set of all prime numbers less than \(8\), \(C =\) The set of even prime numbers. Verify 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:

 

\(B - C =\) $\left\{i,i,i\right\}$

 

\(A \times (B - C) = \{\) \(\}\)

 

\(A \times B = \{\) \(\}\)

 

\(A \times C =\{\) \(\}\)

 

 

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

 

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