Smallest Equivalence Relation on Set \( A = \{1,2,3\} \) 📺 Video Explanation 📝 Question Write the smallest equivalence relation on the set: \[ A = \{1,2,3\} \] ✅ Solution 🔹 Definition An equivalence relation must be: Reflexive Symmetric Transitive The smallest such relation contains only the minimum required pairs. 🔹 Step 1: Reflexive Requirement […]
Write the smallest equivalence relation on the set A = {1, 2, 3}. Read More »
Relation \( 2a + 3b = 30 \) on \( \mathbb{N} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined as: \[ aRb \iff 2a + 3b = 30 \] Write \( R \) as a set of ordered pairs. ✅ Solution 🔹 Step 1: Express a
Check Reflexive, Symmetric and Transitive 📺 Video Explanation 📝 Question Let: \[ A = \{0,1,2,3\} \] \[ R = \{(0,0), (0,1), (0,3), (1,0), (1,1), (2,2), (3,0), (3,3)\} \] Check whether \( R \) is reflexive, symmetric and transitive. ✅ Solution 🔹 Step 1: Reflexive Reflexive requires: \[ (a,a) \in R \quad \forall a \in A
Smallest Equivalence Relation Extension 📺 Video Explanation 📝 Question Let: \[ A = \{1,2,3\} \] Given relation: \[ R = \{(1,1), (2,2), (3,3), (1,3)\} \] Write the ordered pairs to be added to make the smallest equivalence relation. ✅ Solution 🔹 Step 1: Check Reflexive All elements: \[ (1,1), (2,2), (3,3) \] are already present.
Relation \( 2 \mid (a – b) \) on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (a,b) \in R \iff 2 \mid (a – b) \] Show that \( R \) is an equivalence relation. Also find the equivalence class \(
Range of Relation \( R = \{(a, a^3)\} \) 📺 Video Explanation 📝 Question Let relation \( R \) be defined as: \[ R = \{(a, a^3) : a \text{ is a prime number less than } 5\} \] Find the range of \( R \). ✅ Solution 🔹 Step 1: Find Prime Numbers Less
Let R = {(a, a^3) : a is a prime number less than 5} be a relation. Find the range of R. Read More »
Why Relation is Not Transitive 📺 Video Explanation 📝 Question Let relation \( R \) on set \( \{1,2,3\} \) be: \[ R = \{(1,2), (2,1)\} \] State the reason why \( R \) is not transitive. ✅ Solution 🔹 Definition of Transitive Relation A relation \( R \) is transitive if: \[ (a,b) \in
Relation “a is a Divisor of b” from A to B 📺 Video Explanation 📝 Question Let: \[ A = \{2,3,4,5\}, \quad B = \{1,3,4\} \] Relation \( R \) is defined as: \[ (a,b) \in R \iff a \text{ divides } b \] Write \( R \) as a set of ordered pairs. ✅
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