Question

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

• A. \(\frac{3}{2}\)
• B. \(\frac{8}{3}\)
• C. \(\frac{4}{3}\)
• D. \(\frac{3}{4}\)
• E. \(\frac{3}{8}\)

Answer 1

Answer: (E)

Given the binary operation $\circ$ defined as $a \circ b = \frac{a}{b}$, we can solve the expression step by step: 1. First, calculate $3 \circ 4$: \[ 3 \circ 4 = \frac{3}{4} \] 2. Next, calculate $2 \circ (3 \circ 4)$: \[ 2 \circ \left( \frac{3}{4} \right) = \frac{2}{\frac{3}{4}} = 2 \times \frac{4}{3} = \frac{8}{3} \] 3. Finally, calculate $1 \circ (2 \circ (3 \circ 4))$: \[ 1 \circ \left( \frac{8}{3} \right) = \frac{1}{\frac{8}{3}} = 1 \times \frac{3}{8} = \frac{3}{8} \]

The correct option is (E) : \(\frac{3}{8}\)

Answer 2

We are given the binary operation \(a \odot b = \frac{a}{b}\) on Q - {0}. We want to find \(1 \odot (2 \odot (3 \odot 4))\).

First, we evaluate the innermost expression: \(3 \odot 4 = \frac{3}{4}\).

Next, we evaluate \(2 \odot (3 \odot 4) = 2 \odot \frac{3}{4} = \frac{2}{\frac{3}{4}} = 2 \cdot \frac{4}{3} = \frac{8}{3}\).

Finally, we evaluate \(1 \odot (2 \odot (3 \odot 4)) = 1 \odot \frac{8}{3} = \frac{1}{\frac{8}{3}} = 1 \cdot \frac{3}{8} = \frac{3}{8}\).

Therefore, \(1 \odot (2 \odot (3 \odot 4))\) is equal to \(\frac{3}{8}\).