PDF chapter test TRY NOW

Let \(A = \{x \in \mathbb{W}|x < 2\}\), \(B = \{x \in \mathbb{N}|1 < x \leq 4\}\) and \(C = \{3,5\}\). Then verify that \(A \times (B \cap C) = (A \times B) \cap (A \times C)\)
 
Answer:
 
To prove:
 
\(A \times (B \cap C) = (A \times B) \cap (A \times C)\)
 
Explanation:
 
\(B \cap C =\) \(\{\)​​\(\}\)
 
\(A \times (B \cap C) =\) \(\{\)​​\(\}\)
 
\(A \times B = \{\)\(\}\)
 
\(A \times C = \{\)\(\}\)
 
\((A \times B) \cap (A \times C) = \{\)\(\}\)
 
As a result, \(A \times (B \cap C) = (A \times B) \cap (A \times C)\)
 
Hence, we proved.
 
[Note: Enter the first and the second coordinates of the ordered pairs in the increasing order.]