CBSE · Class 11 · Mathematics · Relations and FunctionsIf $A = \{1, 2, 3\}$ and $B = \{3, 4\}$, then $(A \cup B) \times (A \cap B)$ is:
Step-by-Step Solution
To find $(A \cup B) \times (A \cap B)$, first find the union and intersection of sets A and B. $A \cup B = {1, 2, 3, 4}$ and $A \cap B = {3}$. Then the Cartesian product is ${1, 2, 3, 4} \times {3} = {(1, 3), (2, 3), (3, 3), (4, 3)}$. Therefore, the correct option is C.
Detailed Options Breakdown
Option : {(1, 3), (2, 3)}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
Option 1: {(1, 3), (2, 3), (3, 3)}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
Option 2: {(1, 3), (2, 3), (3, 3), (4, 3)} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: {(1, 4), (2, 4), (3, 4)}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
💡 Study Guide: This question tests core syllabus concepts from Relations and Functions. For formulas, key summaries, and mock exam reference guides, read the full Relations and Functions Revision Notes.