April 2026

Constructing Relations with Given Properties 📺 Video Explanation 📝 Question Let \( A = \{1,2,3,4\} \). Construct relations on \( A \) which satisfy: (i) Reflexive and transitive but not symmetric (ii) Symmetric but neither reflexive nor transitive (iii) Reflexive, symmetric and transitive ✅ Solution 🔹 (i) Reflexive and Transitive but Not Symmetric Take: \[ […]

Identity Relation is Reflexive but Converse is Not True 📺 Video Explanation 📝 Statement Prove that every identity relation on a set is reflexive, but the converse is not necessarily true. ✅ Proof 🔹 Part 1: Identity Relation is Reflexive Let \( A \) be a set. The identity relation on \( A \) is:

Relation Defined by \( a \leq b^3 \) on \( \mathbb{R} \) 📺 Video Explanation 📝 Question Let \( R \) be a relation on \( \mathbb{R} \) defined by: \[ (a, b) \in R \iff a \leq b^3 \] Check whether \( R \) is reflexive, symmetric, and transitive. ✅ Solution 🔹 Step 1:

Relation Defined by \( b = a + 1 \) on Set \( A = \{1,2,3,4,5,6\} \) 📺 Video Explanation 📝 Question Let \( A = \{1,2,3,4,5,6\} \). Define relation: \[ R = \{(a,b) : b = a + 1\} \] Check whether \( R \) is reflexive, symmetric, and transitive. ✅ Solution 🔹 Step

Relations Defined on Real Numbers 📺 Video Explanation 📝 Question Relations on \( \mathbb{R} \) are defined as: (i) \( aRb \iff a – b > 0 \) (ii) \( aRb \iff 1 + ab > 0 \) (iii) \( aRb \iff |a| \leq b \) Check whether each relation is reflexive, symmetric, and transitive.

Checking Reflexive, Symmetric and Transitive Relations 📺 Video Explanation 📝 Question Let \( A = \{1,2,3\} \) \( R_1 = \{(1,1), (1,3), (3,1), (2,2), (2,1), (3,3)\} \) \( R_2 = \{(2,2), (3,1), (1,3)\} \) \( R_3 = \{(1,3), (3,3)\} \) Check whether each relation is reflexive, symmetric and transitive. ✅ Solution 🔹 Relation \( R_1

Relation Defined by \( a^2 – 4ab + 3b^2 = 0 \) on \( \mathbb{R} \) 📺 Video Explanation 📝 Question Let \( R_3 \) be a relation on \( \mathbb{R} \) defined by: \[ (a, b) \in R_3 \iff a^2 – 4ab + 3b^2 = 0 \] Test whether \( R_3 \) is reflexive,

Relation Defined by \( |a – b| \leq 5 \) on \( \mathbb{Z} \) 📺 Video Explanation 📝 Question Let \( R_2 \) be a relation on \( \mathbb{Z} \) (set of integers) defined by: \[ (a, b) \in R_2 \iff |a – b| \leq 5 \] Test whether \( R_2 \) is reflexive, symmetric,

Relation Defined by \( a = \frac{1}{b} \) on \( Q_0 \) 📺 Video Explanation 📝 Question Let \( R_1 \) be a relation on \( Q_0 \) (set of non-zero rational numbers) defined by: \[ (a, b) \in R_1 \iff a = \frac{1}{b} \] Test whether \( R_1 \) is reflexive, symmetric, and transitive.

Checking Reflexive, Symmetric and Transitive Relations 📺 Video Explanation 📝 Question Let \( A = \{a, b, c\} \). Relations are defined as: \( R_1 = \{(a,a), (a,b), (a,c), (b,b), (b,c), (c,a), (c,b), (c,c)\} \) \( R_2 = \{(a,a)\} \) \( R_3 = \{(b,a)\} \) \( R_4 = \{(a,b), (b,c), (c,a)\} \) Check whether each