PDF chapter test TRY NOW

1. If \(A = \{5,6\}\), \(B = \{4,5,6\}\), \(C = \{5,6,7\}\). Show that \(A \times A = (B \times B) \cap (C \times C)\)
 
Answer:
 
\(A \times A =\) \(\{\)\(\}\)
 
\(B \times B =\) \(\{\)\(\}\)
 
\(C \times C =\) \(\{\)\(\}\)
 
\((B \times B) \cap (C \times C) =\) \(\{\)\(\}\)
 
Therefore, \(A \times A = (B \times B) \cap (C \times C)\).
 
Hence, we proved.
 
[Note: Enter the first and the second coordinates of the ordered pairs in the increasing order.]
 
2. 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:
 
\(A \cap C = \{\)\(\}\)
 
\(B \cap D =\) i,i
 
\((A \cap C) \times (B \cap D) = \{\)\(\}\)
 
\(A \times B = \{\)\(\}\)
 
\(C \times D = \{\)\(\}\)
 
\((A \times B) \cap (C \times D) = \{\)\(\}\)
 
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.]