Let a set A = A 1 ∪ A 2 ∪ ldots ∪ A k prime where Ai ∩ Aj=φ for i ≠ j 1 ≤ i, j ≤ k. Define the relation R from A to A by R= (x, y): y ∈ Ai. if and only if .x ∈ Ai, 1 ≤ i ≤ k . Then, R is :

Question

Let a set A = A 1 ∪ A 2 ∪ ldots ∪ A k prime where Ai ∩ Aj=φ for i ≠ j 1 ≤ i, j ≤ k. Define the relation R from A to A by R= (x, y): y ∈ Ai. if and only if .x ∈ Ai, 1 ≤ i ≤ k . Then, R is : (A) reflexive, symmetric but not transitive (B) reflexive, transitive but not symmetric (C) reflexive but not symmetric and transitive (D) an equivalence relation

Tardigrade Admin · Accepted Answer

A= 1,2,3 R= (1,1),(1,2),(1,3)(2,1),(2,2),(2,3)(3,1)(3,2)(3,3)

Q. Let a set $A = A_{1} \cup A_{2} \cup \dots \cup A_{k^{'}}$ where $A_{i} \cap A_{j} = ϕ$ for $i \neq = j 1 \leq i, j \leq k$ . Define the relation $R$ from $A$ to $A$ by $R = {(x, y) : y \in A_{i}$ if and only if $x \in A_{i}, 1 \leq i \leq k}$ . Then, $R$ is :

reflexive, symmetric but not transitive

reflexive, transitive but not symmetric

reflexive but not symmetric and transitive

an equivalence relation

$A = {1, 2, 3}$
$R = {(1, 1), (1, 2), (1, 3) (2, 1), (2, 2), (2, 3) (3, 1) (3, 2) (3, 3)}$

Q. Let a set A=A1​∪A2​∪…∪Ak′​ where Ai​∩Aj​=ϕ for i=j1≤i,j≤k. Define the relation R from A to A by R={(x,y):y∈Ai​ if and only if x∈Ai​,1≤i≤k}. Then, R is :