Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.	Let A = {1, 2, 3, … 9} and R be the relation in A x A defined by (a, b) R (c, d). If a + d = b + c for a, b, c, d ∈ A, prove that R is an equivalence relation. Also obtain the equivalence class (2, 5).
Answer» Prove reflexive, prove symmetric and prove transitive R is reflexive, symmetric and transitive, so R is an equivalence relation. Equivalence class (2, 5) is (p, q) ⇒ 2 + q = 5 + p So (1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)

Let A = {1, 2, 3, … 9} and R be the relation in A x A defined by (a, b) R (c, d). If a + d = b + c for a, b, c, d ∈ A, prove that R is an equivalence relation. Also obtain the equivalence class (2, 5).

Answer»

Prove reflexive, prove symmetric and prove transitive

R is reflexive, symmetric and transitive, so

R is an equivalence relation.

Equivalence class (2, 5) is (p, q) ⇒ 2 + q = 5 + p

So (1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)

Discussion