Question
Download Solution PDFIf A = {1, 2, 3, 4, 5}, then the relation R = {(2, 3), (3, 4), (2, 4)} on A is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
If A = {1, 2, 3, 4, 5}, then the relation R = {(2, 3), (3, 4), (2, 4)} on A
Concept:
IF A is a set and R be a relation defined on A then
R is Reflexive: a is related to a. ∀ a ∈ A
R is symmetric: if a is related to b, then b is related to a. ∀ a, b ∈ A
R is transitive: if a is related to b and b is related to c then a is related to c. ∀ a, b, c ∈ A
Calculation:
If A = {1, 2, 3, 4, 5}, then the relation R = {(2, 3), (3, 4), (2, 4)} on A
1. Reflexive :
Let 1 ∈ A but (1, 1) ∉ R .
Hence R is not Reflexive.
2. Symmetric :
Let 2, 3 ∈ A and (2, 3) ∈ R but (3, 2) ∉ R
Hence R is not Symmetric.
3. Transitive :
Let 2 , 3, 4 ∈ A and
( 2, 3) and (3, 4) ∈ R then ( 2, 4 ) ∈ R
Hence R is transitive.
Hence R is transitive only.
Hence the option (1) is correct.
Last updated on May 26, 2025
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