true or false,if true give proofs, false then find exampleR[a,b] is defined

the regulated function on [a,b])

(a) f∉ R[a,b] implies |f|∉ R[a.b]

(b)|f|∉

R[a,b] implies f∉ R[a,b]

(c)f∈R[a.b], g∉ R[a,b] imply f+g ∉R[a,b]

i do need some helps in 3 statement cause i dont know how to begin.