Let A be the set of all functions f: Z → Z and R be a relation on A such that R = \(f,g): f(0)=g(1) and f(1)=g(0). Then R is:

(B) Symmetric but neither reflective nor transitive

(A) Symmetric and transitive but not reflective

(C) Reflexive but neither symmetric nor transitive

(D) Transitive but neither reflexive nor symmetric

Sets, Relations and Functions: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q37

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let

A

be the set of all functions

f: \mathbb{Z} \to \mathbb{Z}

and

R

be a relation on

A

such that

R = \{(f,g): f(0)=g(1) \text{ and } f(1)=g(0)\}

. Then

R

is: