14. Five marks exercise problems VI

Given \(A = \{1,2,3\}\), \(B = \{2,3,5\}\), \(C = \{3,4\}\) and \(D = \{1,3,5\}\), check if \((A \cap C) \times (B \cap D) = (A \times B) \cap (C \times D)\) is true?

 

Answer:

 

\(A \cap C = \{\)\(\}\)

 

\(B \cap D =\) $\left\{i,i\right\}$

 

\((A \cap C) \times (B \cap D) = \{\) \(\}\)

 

\(A \times B = \{\) \(\}\)

 

\(C \times D = \{\) \(\}\)

 

\((A \times B) \cap (C \times D) = \{\) \(\}\)

 

Therefore, \((A \cap C) \times (B \cap D) = (A \times B) \cap (C \times D)\) is true.

 

[Note: Enter the first and the second coordinates of the ordered pairs in the increasing order.]