Binary Operation on Rational Numbers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( * \) on \( \mathbb{Q} \) defined by \( a * b = \frac{a – 1}{b + 1} \quad \forall \, a, b \in \mathbb{Q} \) Concept: A binary operation must be […]
Binary Operation on Natural Numbers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( O \) on \( \mathbb{N} \) defined by \( a \, O \, b = a^b + b^a \quad \forall \, a, b \in \mathbb{N} \) Concept: A binary operation on a
Binary Operation Modulo 6 Addition 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: A set \( S = \{0,1,2,3,4,5\} \) and an operation \( +_6 \) defined by \[ a +_6 b = \begin{cases} a + b, & \text{if } a + b < 6 \\ a +
Binary Operation Modulo 6 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: A set \( S = \{1,2,3,4,5\} \) and an operation \( \times_6 \) defined by \( a \times_6 b = \text{remainder when } ab \text{ is divided by } 6 \) Concept: A binary operation on
Binary Operation on Natural Numbers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( * \) on \( \mathbb{N} \) defined by \( a * b = a + b – 2 \quad \forall \, a, b \in \mathbb{N} \) Concept: A binary operation on a
Binary Operation on Integers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( O \) on \( \mathbb{Z} \) defined by \( a \, O \, b = ab \quad \forall \, a, b \in \mathbb{Z} \) Concept: A binary operation on a set satisfies the
Binary Operation on Natural Numbers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( * \) on \( \mathbb{N} \) defined by \( a * b = ab \quad \forall \, a, b \in \mathbb{N} \) Concept: A binary operation on a set is a rule
Rational Function Type Check One-One / Onto 🎥 Video Explanation 📝 Question \[ f:\mathbb{R}\setminus\left\{\frac{3}{5}\right\} \to \mathbb{R}, \quad f(x)=\frac{3x+2}{5x-3} \] Determine whether \(f\) is one-one and/or onto. ✅ Solution 🔹 Step 1: Check Injective Let \(f(x_1)=f(x_2)\): \[ \frac{3x_1+2}{5x_1-3}=\frac{3x_2+2}{5x_2-3} \] Cross multiply: \[ (3x_1+2)(5x_2-3)=(3x_2+2)(5x_1-3) \] Simplifying gives: \[ x_1=x_2 \] ✔️ Function is one-one — 🔹 Step
Let f : R-{3/5}→R be defined by f(x) = (3x+2)/(5x-3) . Then, Read More »
Injective Functions Number of One-One Functions 🎥 Video Explanation 📝 Question Set \(A\) has 7 elements and set \(B\) has 10 elements. Find number of one-one functions from \(A\) to \(B\). (a) \({}^{10}C_7\) (b) \({}^{10}C_7 \times 7!\) (c) \(7^{10}\) (d) \(10^7\) ✅ Solution 🔹 Step 1: Formula for One-One Functions Number of injective functions from
Bijective Functions Number of One-One and Onto Mappings 🎥 Video Explanation 📝 Question Let set \(A\) have 5 elements and set \(B\) have 6 elements. Find number of one-one and onto mappings from \(A\) to \(B\). A. 720 B. 120 C. 0 D. none of these ✅ Solution 🔹 Step 1: Condition for Bijective Function