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: \[
If R is a symmetric relation on a set A, then write a relation between R and R^{-1}. Read More »
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
If R = {(x,y) : x + 2y = 8} is a relation on N, then write the range of R. Read More »
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: \[ (a,a) \in R \quad \forall a \in A \]
Write the smallest reflexive relation of set A = {1, 2, 3, 4}. Read More »
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,
Write the identity relation of set A = {a, b, c}. Read More »
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
If R = {( x ,y): x^2 + y^2 ≤ 4; x ,y ϵ Z} is a relation of Z, write the domain of R. Read More »
Domain of Relation \( a^2 + b^2 = 25 \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (a,b) \in R \iff a^2 + b^2 = 25 \] Find the domain of \( R \). ✅ Solution 🔹 Step 1: Understand Domain Domain = set