Question:
If A = 2 and B = 4, what is the value of \(@(/(*(A, B), B), A)\)?
If A = 2 and B = 4, what is the value of \(@(/(*(A, B), B), A)\)?
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Evaluate inner-most functions first when parsing nested operations.
Updated On: Aug 6, 2025
- 2
- 4
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The Correct Option is A
Solution and Explanation
Given definitions:
- \( @(A, B) = \frac{A + B}{2} \) (average)
- \( *(A, B) = A \times B \) (product)
- \( /(A, B) = \frac{A}{B} \) (division)
Given:
\[
@(/(*(A, B), B), A)
\]
Step-by-step:
- \( A = 2, B = 4 \)
- \( *(A, B) = 2 \times 4 = 8 \)
- \( /(8, B) = \frac{8}{4} = 2 \)
- \( @(2, A) = \frac{2 + 2}{2} = \frac{4}{2} = \boxed{2} \)
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Top Questions on Relations
- A classroom teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set \( A = \{1, 2, 3\} \): \[ R_1 = \{(2, 3), (3, 2)\}, \quad R_2 = \{(1, 2), (1, 3), (3, 2)\}, \quad R_3 = \{(1, 2), (2, 1), (1, 1)\}, \] \[ R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}, \quad R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}. \] The students are asked to answer the following questions about the above relations:
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OR
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Reason (R): The number \( 2n \) is composite for all natural numbers \( n \). - The relation \( R = \{(a, a), (b, b), (c, c), (a, c)\ \) defined on the set \( \{a, b, c\} \) is _____________.}
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