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 \cup C) = (A \times B) \cup (A \times C)
 
Answer:
 
To prove:
 
A \times (B \cup C) = (A \times B) \cup (A \times C)
 
Explanation:
 
B \cup C = \{\}
 
A \times (B \cup C) = \{\}
 
A \times B = \{\}
 
A \times C = \{\}
 
(A \times B) \cup (A \times C) = \{\}
 
As a result, A \times (B \cup C) = (A \times B) \cup (A \times C)
 
Hence, we proved.
 
[Note: Enter the first and the second coordinates of the ordered pairs in the increasing order.]