Question:
If $a \wedge b = a^2 + b^3 - ab$ and $a \vee b = a^3 + b^2 + ab$, then what is $(1 \wedge 2) \vee (1 \vee 2)$?
If $a \wedge b = a^2 + b^3 - ab$ and $a \vee b = a^3 + b^2 + ab$, then what is $(1 \wedge 2) \vee (1 \vee 2)$?
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In operation-based questions, solve inner operations first, then substitute step by step.
Updated On: Apr 21, 2026
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The Correct Option is B
Solution and Explanation
Concept:
Evaluate step by step using given operations.
Step 1: Find $1 \wedge 2$.
\[ 1 \wedge 2 = 1^2 + 2^3 - (1)(2) = 1 + 8 - 2 = 7 \]
Step 2: Find $1 \vee 2$.
\[ 1 \vee 2 = 1^3 + 2^2 + (1)(2) = 1 + 4 + 2 = 7 \]
Step 3: Find $(1 \wedge 2) \vee (1 \vee 2)$.
\[ 7 \vee 7 = 7^3 + 7^2 + 7 \cdot 7 = 343 + 49 + 49 = 441 \]
Hence, the value is 441.
Step 1: Find $1 \wedge 2$.
\[ 1 \wedge 2 = 1^2 + 2^3 - (1)(2) = 1 + 8 - 2 = 7 \]
Step 2: Find $1 \vee 2$.
\[ 1 \vee 2 = 1^3 + 2^2 + (1)(2) = 1 + 4 + 2 = 7 \]
Step 3: Find $(1 \wedge 2) \vee (1 \vee 2)$.
\[ 7 \vee 7 = 7^3 + 7^2 + 7 \cdot 7 = 343 + 49 + 49 = 441 \]
Hence, the value is 441.
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