Range of Relation from \( A \) to \( B \) Defined by \( x>y \) 📺 Video Explanation 📝 Question Let: \[ A=\{1,2,3\}, \quad B=\{1,4,5,9\} \] A relation \( R \) from \( A \) to \( B \) is defined by: \[ xRy \iff x>y \] Find the range of \( R \). […]
Relation on \( \mathbb{N}\times\mathbb{N} \) Defined by \( a+d=b+c \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N}\times\mathbb{N} \) be defined by: \[ (a,b)\,R\,(c,d)\iff a+d=b+c \] Then, \( R \) is: (a) reflexive but not symmetric (b) reflexive and transitive but not symmetric (c) an equivalence relation (d) none of
Count Relations on \( A=\{1,2,3\} \) That Are Reflexive, Symmetric but Not Transitive 📺 Video Explanation 📝 Question Let \[ A=\{1,2,3\} \] Find the number of relations on \( A \) which: contain \((1,2)\) and \((1,3)\) are reflexive are symmetric but are not transitive ✅ Solution 🔹 Step 1: Reflexive condition For reflexive relation, all
Equivalence Class of \( (3,2) \) in \( A \times A \) 📺 Video Explanation 📝 Question Let \[ A=\{2,3,4,5,\dots,18\} \] An equivalence relation \( \simeq \) on \( A\times A \) is defined by: \[ (a,b)\simeq(c,d)\iff ad=bc \] Find the number of ordered pairs in the equivalence class of: \[ (3,2) \] ✅ Solution
Relation \( R=\{(b,c)\} \) on Set \( A=\{a,b,c\} \) 📺 Video Explanation 📝 Question Let \[ A=\{a,b,c\} \] and relation \[ R=\{(b,c)\} \] on \( A \). Then \( R \) is: (a) reflexive only (b) symmetric only (c) transitive only (d) reflexive and transitive only ✅ Solution We check reflexive, symmetric, and transitive properties.
Relation of Perpendicular Lines in a Plane 📺 Video Explanation 📝 Question Let \( R \) be a relation on the set of all straight lines in a plane such that: \[ L_1 \, R \, L_2 \iff L_1 \perp L_2 \] Then, \( R \) is: (a) symmetric (b) reflexive (c) transitive (d) an
Relation on Set \( A=\{1,2,3,4,5\} \) Defined by \( |a^2-b^2|
Relation \( |x-y| \leq 1 \) on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let \( R \) be a relation on the set of integers \( \mathbb{Z} \) defined by: \[ (x,y)\in R \iff |x-y|\leq 1 \] Then, \( R \) is: (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and
Which of the Following is Not an Equivalence Relation on \( \mathbb{Z} \)? 📺 Video Explanation 📝 Question Which of the following is not an equivalence relation on \( \mathbb{Z} \)? (a) \( aRb \iff a+b \text{ is an even integer} \) (b) \( aRb \iff a-b \text{ is an even integer} \) (c) \(
Check Ordered Pairs in Relation 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined as: \[ (a,b) \in R \iff a = b – 2,\quad b > 6 \] Check which of the following belongs to \( R \): (a) \( (2,4) \) (b) \( (3,8) \) (c)