Let \(A =\) The set of all natural numbers less than \(5\), \(B =\) The set of all prime numbers less than \(9\), \(C =\) 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:
\(B - C =\)
\(A \times (B - C) =\)
\(A \times B =\)
\(A \times C =\)
\((A \times B) - (A \times C) =\)
Therefore, \(A \times (B - C) = (A \times B) - (A \times C)\)
Hence, we proved.
Answer variants:
\(\{3,5,7\}\)