For each of the following statements, determine whether it istrue or false and justify your answer.
a. If the function f + g: IR --> IR is continuous, then thefunctions f :IR --> IR and g :IR --> IR also arecontinuous.
b. If the function f^2 : IR --> R is continuous, then so is thefunction f :R --> IR.
c. If the functions f + g: IR and g: IR --> IR are continuous,then so is the function f :IR --> IR.
d. Every function f: N --> IR is continuous, where N denotes theset of natural numbers.
