April 2026

Relation “y is One Half of x” on Set \( A \) 📺 Video Explanation 📝 Question Let: \[ A = \{1,2,3,4,5,6,7,8\} \] Relation \( R \) is defined as: \[ R = \{(x,y) : y \text{ is one half of } x,\ x,y \in A\} \] Write \( R \) as a set of […]

Relation “Less Than” from A to B 📺 Video Explanation 📝 Question Let: \[ A = \{3,5,7\}, \quad B = \{2,4,9\} \] Relation \( R \) is defined as: \[ R = \{(x,y) : x \in A,\ y \in B,\ x < y\} \] Write \( R \) as a set of ordered pairs. ✅

Relation Based on Relatively Prime Numbers 📺 Video Explanation 📝 Question Let: \[ A = \{3,5,7\}, \quad B = \{2,6,10\} \] Relation \( R \) is defined as: \[ R = \{(x,y) : x \in A,\ y \in B,\ \gcd(x,y) = 1\} \] Find \( R \) and \( R^{-1} \). ✅ Solution 🔹 Step

Inverse Relation \( R^{-1} \) 📺 Video Explanation 📝 Question Let: \[ A = \{2,3,4\}, \quad B = \{1,3,7\} \] Relation \( R \) is defined as: \[ R = \{(x,y) : x \in A,\ y \in B,\ x < y\} \] Find \( R^{-1} \). ✅ Solution 🔹 Step 1: Find Relation \( R

Relation \( |x^2 – y^2| < 1 \) on \( A = \{1,2,3,4,5\} \) 📺 Video Explanation 📝 Question Let relation \( R \) on set \( A = \{1,2,3,4,5\} \) be defined as: \[ (x,y) \in R \iff |x^2 – y^2| < 1 \] Write \( R \) as a set of ordered pairs.

Relation Between \( R \) and \( R^{-1} \) 📺 Video Explanation 📝 Question If \( R \) is a symmetric relation on a set \( A \), find the relation between \( R \) and \( R^{-1} \). ✅ Solution 🔹 Definition of Symmetric Relation A relation \( R \) is symmetric if: \[

Range of Relation \( x + 2y = 8 \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined as: \[ (x,y) \in R \iff x + 2y = 8 \] Find the range of \( R \). ✅ Solution 🔹 Step 1: Express x in terms of

Smallest Reflexive Relation on Set \( A = \{1,2,3,4\} \) 📺 Video Explanation 📝 Question Write the smallest reflexive relation on the set: \[ A = \{1,2,3,4\} \] ✅ Solution 🔹 Definition A relation \( R \) on set \( A \) is reflexive if: \[ (a,a) \in R \quad \forall a \in A \]

Identity Relation on Set \( A = \{a, b, c\} \) 📺 Video Explanation 📝 Question Write the identity relation on the set: \[ A = \{a, b, c\} \] ✅ Solution 🔹 Definition The identity relation on a set \( A \) is: \[ R = \{(x,x) : x \in A\} \] That is,

Domain of Relation \( x^2 + y^2 \le 4 \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (x,y) \in R \iff x^2 + y^2 \le 4 \] Find the domain of \( R \). ✅ Solution 🔹 Step 1: Understand Domain Domain = set