April 2026

Relation \( ab\geq0 \) on Real Numbers 📺 Video Explanation 📝 Question Let relation \( S \) on the set of real numbers \( \mathbb{R} \) be defined by: \[ (a,b)\in S \iff ab\geq0 \] Then, \( S \) is: A. symmetric and transitive only B. reflexive and symmetric only C. antisymmetric relation D. an […]

Relation \( R=\{(a,b),(b,a),(a,a)\} \) on Set \( A=\{a,b,c,d\} \) 📺 Video Explanation 📝 Question Let \[ A=\{a,b,c,d\} \] and: \[ R=\{(a,b),(b,a),(a,a)\} \] Then \(R\) is: A. symmetric and transitive only B. reflexive and transitive only C. symmetric only D. transitive only ✅ Solution 🔹 Reflexive Check For reflexive relation, all self-pairs must be present: \[

Identity Relation on Set \( A=\{1,2,3\} \) 📺 Video Explanation 📝 Question Let: \[ A=\{1,2,3\} \] and relation: \[ R=\{(1,1),(2,2),(3,3)\} \] Then, \(R\) is: (a) reflexive (b) symmetric (c) transitive (d) all the three options ✅ Solution This relation is the identity relation on set \(A\). 🔹 Reflexive A relation is reflexive if all self-pairs

Relation on \( A=\{1,2,3,4,5,6,7,8,9\} \) Defined by \( y=3x \) 📺 Video Explanation 📝 Question Let \[ A=\{1,2,3,4,5,6,7,8,9\} \] A relation \(R\) on \(A\) is defined by: \[ xRy \iff y=3x \] Find \(R\). (a) \(\{(3,1),(6,2),(8,2),(9,3)\}\) (b) \(\{(3,1),(6,2),(9,3)\}\) (c) \(\{(3,1),(2,6),(3,9)\}\) (d) none of these ✅ Solution Relation means all ordered pairs \((x,y)\in A\times A\) such

Largest Equivalence Relation on a Set 📺 Video Explanation 📝 Question If \(R\) is the largest equivalence relation on a set \(A\) and \(S\) is any relation on \(A\), then: A. \(R \subset S\) B. \(S \subset R\) C. \(R=S\) D. none of these ✅ Solution 🔹 Largest Equivalence Relation The largest equivalence relation on

Relation \( R=\{(1,2),(2,3),(1,3)\} \) on Set \( A=\{1,2,3\} \) 📺 Video Explanation 📝 Question Let \[ A=\{1,2,3\} \] and: \[ R=\{(1,2),(2,3),(1,3)\} \] Then, \(R\) is: (a) neither reflexive nor transitive (b) neither symmetric nor transitive (c) transitive (d) none of these ✅ Solution 🔹 Reflexive Check For reflexive relation: \[ (1,1),(2,2),(3,3) \] must be present.

Relation on Set \( A=\{a,b,c\} \) 📺 Video Explanation 📝 Question Let \[ A=\{a,b,c\} \] and relation \[ R=\{(a,a),(b,b),(c,c),(a,b)\} \] Then, \(R\) is: (a) identity relation (b) reflexive (c) symmetric (d) equivalence relation ✅ Solution 🔹 Check Identity Relation Identity relation on \(A\) is: \[ I=\{(a,a),(b,b),(c,c)\} \] But \(R\) also contains: \[ (a,b) \] So:

Inverse Relation Defined by \( y=x-3 \) 📺 Video Explanation 📝 Question A relation \( R \) is defined from: \[ A=\{11,12,13\}, \quad B=\{8,10,12\} \] by: \[ y=x-3 \] Find the inverse relation \(R^{-1}\). (a) \(\{(8,11),(10,13)\}\) (b) \(\{(11,8),(13,10)\}\) (c) \(\{(10,13),(8,11),(8,10)\}\) (d) none of these ✅ Solution 🔹 Step 1: Find relation \(R\) Relation from \(A\)

Domain of Relation on \( \mathbb{N} \) Defined by \( x+2y=8 \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined by: \[ xRy \iff x+2y=8 \] Find the domain of \( R \). (a) \(\{2,4,8\}\) (b) \(\{2,4,6,8\}\) (c) \(\{2,4,6\}\) (d) \(\{1,2,3,4\}\) ✅ Solution Domain means all values

Relation from \( \mathbb{C} \) to \( \mathbb{R} \) Defined by \( |x|=y \) 📺 Video Explanation 📝 Question A relation \( \phi \) from \( \mathbb{C} \) to \( \mathbb{R} \) is defined by: \[ x \,\phi\, y \iff |x|=y \] Which of the following is correct? (a) \((2+3i)\,\phi\,13\) (b) \(3\,\phi\,(-3)\) (c) \((1+i)\,\phi\,2\) (d)