Which of the following funcitons is/are periodie ?

Options

A. `{:{(1",","x is rational"),(0",","x is irrational"):}`
B. `f(x)={:{(x-[x]",",2n le x lt 2n +1),(1/2,2n+1 le x lt 2n +2):}`, where[.] denotes the greatest integer function, `n in Z`
C. `f(x)= (-1)^([(2x)/(pi)])` where [.] denotes the greatest integer integer function
D. `f(x)=x-[x+3]+tan ((pi x)/(2))`, where [.] denotes the greatest integer function, and a is a rational number

Answer

A, B, C, D