3. For nZ+define R(n)=28n+1+21S(n)=2(R(n)1)(R(n)2) (a) Explain why both R(n) and S(n) are integers. (b) What are the minimal values R(n) and S(n) can take? Now onsider a function f:Z+Z+Z+defined as follows f(n)=(nS(n),R(n)+S(n)n) (c) Note that f(n) is a function from the 1-dimentsional integer grid into the 2-dimensional integer grid. Write a Scheme program which calculates the values f(n) for n= 1,2,,15 and plot those values on the coordinate plane marking each grid point by the argument n the grid point came from. In addition to the chart, cut-andpaste the program you used to calculate the grid points and include it with your submission. Please indicate which function calculates the required grid points. (d) Is f 1-1? Explain your reasoning. (e) Is f onto? Explain your reasoning (f) Based on your results from (c), (d), (e), what can you say about cardinalities of Z+ and Z+Z+? 3. For nZ+define R(n)=28n+1+21S(n)=2(R(n)1)(R(n)2) (a) Explain why both R(n) and S(n) are integers. (b) What are the minimal values R(n) and S(n) can take? Now onsider a function f:Z+Z+Z+defined as follows f(n)=(nS(n),R(n)+S(n)n) (c) Note that f(n) is a function from the 1-dimentsional integer grid into the 2-dimensional integer grid. Write a Scheme program which calculates the values f(n) for n= 1,2,,15 and plot those values on the coordinate plane marking each grid point by the argument n the grid point came from. In addition to the chart, cut-andpaste the program you used to calculate the grid points and include it with your submission. Please indicate which function calculates the required grid points. (d) Is f 1-1? Explain your reasoning. (e) Is f onto? Explain your reasoning (f) Based on your results from (c), (d), (e), what can you say about cardinalities of Z+ and Z+Z+