15. Find f(A) and f'(B) for the given function and sots. (a) :R-Ris defined by f(r)...

 

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15. Find f(A) and f'(B) for the given function and sots. (a) :R-Ris defined by f(r) = r +1, A=[-1,2), B = (0,4). (b) f: R-R is defined by f(r) = sin r, A = (0, ), B= (0,2). (c) f:R-Z is defined by f(r) = L] (the floor function), A = (0, 4), B = (0,1,2}. (d) f:R-(0) R is defined by f(r) =r + - A= [1,5), B= [0, 1). 16. Let f: D-C, A, BC D, E, FCC. Prove each of the following statements. (a) S(AUB) = (A4)U S(B). (b) EUF) =f(E)uf (F). (e) f(ANB) S F(A)ns(B). (d) If f is 1-1, then f(AN B) = f(A)n S(B). %3! (e) If f is 1-1, then A =fS(A). %3D (f) IH ACB, them f(A) S S(B). (2) If (A) S S(B), then AC B is false. (Give a counterexample) (b) II ECF, thenf-(E) S(F). O Er (E) Sr(F), then ECFis fabe. (Give a counterexample) 17. Let f: D-C. A= {A. CD: Va € A), and B= (B, SC: Va E A). (a) Prove f FLA.). (b) (e) Pee that 18. Let X- LA-B) and Y-f(A)-(). (a) Pue or digre the cunjetture X-Y (b) f X+Y, thu pre or disprove the conjertures XGY or YCX. 19. Repeat the previco peulenu ke X-rME-F) and Y- )-F) 15. Find f(A) and f'(B) for the given function and sots. (a) :R-Ris defined by f(r) = r +1, A=[-1,2), B = (0,4). (b) f: R-R is defined by f(r) = sin r, A = (0, ), B= (0,2). (c) f:R-Z is defined by f(r) = L] (the floor function), A = (0, 4), B = (0,1,2}. (d) f:R-(0) R is defined by f(r) =r + - A= [1,5), B= [0, 1). 16. Let f: D-C, A, BC D, E, FCC. Prove each of the following statements. (a) S(AUB) = (A4)U S(B). (b) EUF) =f(E)uf (F). (e) f(ANB) S F(A)ns(B). (d) If f is 1-1, then f(AN B) = f(A)n S(B). %3! (e) If f is 1-1, then A =fS(A). %3D (f) IH ACB, them f(A) S S(B). (2) If (A) S S(B), then AC B is false. (Give a counterexample) (b) II ECF, thenf-(E) S(F). O Er (E) Sr(F), then ECFis fabe. (Give a counterexample) 17. Let f: D-C. A= {A. CD: Va € A), and B= (B, SC: Va E A). (a) Prove f FLA.). (b) (e) Pee that 18. Let X- LA-B) and Y-f(A)-(). (a) Pue or digre the cunjetture X-Y (b) f X+Y, thu pre or disprove the conjertures XGY or YCX. 19. Repeat the previco peulenu ke X-rME-F) and Y- )-F)