UPSKILL MATH PLUS
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Learn moreLet \(A =\) The set of all natural numbers less than \(8\), \(B =\) The set of all prime numbers less than \(8\), \(C =\) The set of even prime numbers. Verify that \((A \cap B) \times C = (A \times C) \cap (B \times C)\)
Answer:
To prove:
\((A \cap B) \times C = (A \times C) \cap (B \times C)\)
Explanation:
\(A \cap B =\)
\((A \cap B) \times C = \{\)\(\}\)
\(A \times C = \{\)\(\}\)
\(B \times C =\{\)\(\}\)
\((A \times C) \cap (B \times C) = \{\)\}\)
As a result, \((A \cap B) \times C = (A \times C) \cap (B \times C)\)
Hence, we proved.
[Note: Enter the first and the second coordinates of the ordered pairs in the increasing order.]