Let R be a relation on the set A of ordered pairs of non-zero integers defined by (x, y) R (u, v) iff xv = yu. Show that R is an equivalence relation.

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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. ✅ […]

Let R be a relation on the set A of ordered pairs of non-zero integers defined by (x, y) R (u, v) iff xv = yu. Show that R is an equivalence relation. Read More »

m is said to be related to n if m and n are integers and m – n is divisible by 13. Does this define an equivalence relation ?

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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.

m is said to be related to n if m and n are integers and m – n is divisible by 13. Does this define an equivalence relation ? Read More »

Let Z be the set of integers. Show that the relation R = {(a, b) : a, b ∈ Z and a + b is even} is an equivalence relation on Z.

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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

Let Z be the set of integers. Show that the relation R = {(a, b) : a, b ∈ Z and a + b is even} is an equivalence relation on Z. Read More »

Let n be a fixed positive integer. Define a relation R on Z as follows : (a, b) ∈ R ⇔ a – b is divisible by n. Show that R is an equivalence relation on Z.

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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

Let n be a fixed positive integer. Define a relation R on Z as follows : (a, b) ∈ R ⇔ a – b is divisible by n. Show that R is an equivalence relation on Z. Read More »

Prove that the relation R on Z defined by (a, b) ∈ R ⇔ a – b is divisible by 5 is an equivalence relation on Z.

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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.

Prove that the relation R on Z defined by (a, b) ∈ R ⇔ a – b is divisible by 5 is an equivalence relation on Z. Read More »

Show that the relation R on the set Z of integers, given by R = {(a, b) : 2 divides a – b}, is an equivalence relation.

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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:

Show that the relation R on the set Z of integers, given by R = {(a, b) : 2 divides a – b}, is an equivalence relation. Read More »

Show that the relation R defined by R = {(a, b): a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.

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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.

Show that the relation R defined by R = {(a, b): a – b is divisible by 3; a, b ∈ Z} is an equivalence relation. Read More »

Relation on N : x + 4y = 10, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive.

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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 on N : x + 4y = 10, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Read More »

Relation on N : xy is square of an integer, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive.

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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 🔹

Relation on N : xy is square of an integer, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Read More »

Relation on N : x + y = 10, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive.

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Relation \( x + y = 10 \) on \( \mathbb{N} \) 📺 Video Explanation 📝 Question Let relation \( R \) on \( \mathbb{N} \) be defined as: \[ (x, y) \in R \iff x + y = 10 \] Check whether \( R \) is reflexive, symmetric, and transitive. ✅ Solution 🔹 Step

Relation on N : x + y = 10, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Read More »