Question:
If \( A = \{1,2\}, B = \{1,2,3,4\}, C = \{5,6\}, D = \{5,6,7,8\} \), then state which of the following is true?
If \( A = \{1,2\}, B = \{1,2,3,4\}, C = \{5,6\}, D = \{5,6,7,8\} \), then state which of the following is true?
Show Hint
Cartesian product follows subset rule: \( A\subset B, C\subset D \Rightarrow A\times C \subset B\times D \).
Updated On: Apr 22, 2026
- \( (A \times C) \subset (B \times D) \)
- \( A \times B \subset C \times D \)
- \( (A \times B) \subset (A \times D) \)
- \( A \times C \subset B \times D \)
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The Correct Option is A
Solution and Explanation
Concept:
If \( A \subset B \) and \( C \subset D \), then:
\[
A \times C \subset B \times D
\]
Step 1: Check subsets.
\[ A \subset B,\quad C \subset D \]
Step 2: Apply property.
\[ A \times C \subset B \times D \]
Step 1: Check subsets.
\[ A \subset B,\quad C \subset D \]
Step 2: Apply property.
\[ A \times C \subset B \times D \]
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