MP Board Class 11 Mathematics — If $P = \{1, 2\}$, form th

MP Board · Class 11 · Mathematics · Relations and FunctionsIf $P = \{1, 2\}$, form the set $P \times P \times P$.

📊Student Analytics & Stats

Total Attempts: 3

Accuracy Rate: 66.7%

Step-by-Step Solution

The Cartesian product of three sets $P \times P \times P$ consists of all ordered triplets $(a, b, c)$ where $a, b, c \in P$. Since $P = {1, 2}$, the number of elements in $P \times P \times P$ is $2 \times 2 \times 2 = 8$. Listing them out gives ${(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)}$. Hence, option B is correct.

Detailed Options Breakdown

Option : {(1,1), (2,2), (1,2)}

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.

Option 1: {(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)} (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 2: {(1,1,1), (2,2,2)}

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.

Option 3: {(1,2), (2,1), (1,1), (2,2)}

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.

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Verified by Academic Committee