Answer the following questions: a) Give an example* of two functions f and g that have all three of the following properties: • f is not a surjection, • g is not an injection, and g•fis a bijection....

Discrete math

Extracted text: Answer the following questions: a) Give an example* of two functions f and g that have all three of the following properties: • f is not a surjection, • g is not an injection, and g•fis a bijection. Please Include a short explanation as to why your example exhibits all three properties. b) Prove by induction: For all natural numbers n 2 4, 2 n < n!,="" where="" n!="" is="" the="" factorial="" operation,="" n!="1·" 2·="" 3·="" ··.="" ·="">