Relation \( a = b \) on Set \( A \) 📺 Video Explanation 📝 Question Let \( A = \{x \in \mathbb{Z} : 0 \le x \le 12\} \). Define relation \( R \) as: \[ R = \{(a,b) : a = b\} \] Show that \( R \) is an equivalence relation. Also […]
Relation \( xv = yu \) on Ordered Pairs 📺 Video Explanation 📝 Question Let \( A \) be the set of ordered pairs of non-zero integers. Define relation \( R \) as: \[ (x, y) \in R (u, v) \iff xv = yu \] Show that \( R \) is an equivalence relation. ✅
Relation \( a – b \) divisible by 13 on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (a, b) \in R \iff a – b \text{ is divisible by } 13 \] Check whether \( R \) defines an equivalence relation.
Relation \( a + b \) is even on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (a, b) \in R \iff a + b \text{ is even} \] Show that \( R \) is an equivalence relation. ✅ Solution 🔹 Step
Relation \( a – b \) divisible by \( n \) on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let \( n \) be a fixed positive integer. Define a relation \( R \) on \( \mathbb{Z} \) as: \[ (a, b) \in R \iff a – b \text{ is divisible by } n
Relation \( a – b \) divisible by 5 on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (a, b) \in R \iff a – b \text{ is divisible by } 5 \] Show that \( R \) is an equivalence relation.
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. ✅ Solution 🔹 Step 1:
Relation \( a – b \) divisible by 3 on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{Z} \) be defined as: \[ (a, b) \in R \iff a – b \text{ is divisible by } 3 \] Show that \( R \) is an equivalence relation.
Relation \( x + 4y = 10 \) on \( \mathbb{N} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined as: \[ (x, y) \in R \iff x + 4y = 10 \] Check whether \( R \) is reflexive, symmetric, and transitive. ✅ Solution 🔹 Step
Relation: \( xy \) is a Perfect Square on \( \mathbb{N} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined as: \[ (x, y) \in R \iff xy \text{ is a perfect square} \] Check whether \( R \) is reflexive, symmetric, and transitive. ✅ Solution 🔹