Please do Exercise 16.1.6 part ABC and show step by step and explain Exercise 16.1.6.550CHAPTER 16 FURTHER TOPICS IN CRYPTOGRAPHY(a) We may define a function f : Z7\ {0} → Z7\ {0} by the equation:f(n)= mod(2,7). Use parts (a) and (b) of Exercise 16.1.5 to provethat f is neither one-to-one nor onto.(b) We may also define a function g: Z7\ {0} → Z7\ {0} by the equation:g(n)= mod (3, 7). Prove or disprove: g is one-to-one.(c) With the same g as in part (b), prove or disprove: g is onto. In previous math courses you learned that the inverse operation of expo-nentiation is taking the logarithm: for example, 23 = 8 while log₂ 8 = 3. Itis possible to do the same with discrete exponentiation: an inverse operationto discrete exponentiation is referred to as 'finding a discrete logarithmor (DL)'. Note that since discrete exponentiation involves raising to a powerwhich is a natural number, a DL will always be a natural number. For ex-ample, since mod (25, 7) = 4, we could say that under multiplication mod 7,5 is a DL of 4 with base 2.Now why have we been saying, "a DL" rather than "the DL"? Becausethere happens to be more than one:Exercise 16.1.5.(a) Find all natural numbers n such that mod (2", 7) = 4. Use your resultto complete the following sentence: "Under multiplication mod 7, thediscrete logarithm(s) of 4 with base 2 are ...."(b) Find all natural numbers n such that mod (2, 7) = 3. Use your resultto complete the following sentence: "Under multiplication mod 7, thediscrete logarithm(s) of 3 with base 2 are ...."(c) Find all nonzero elements of Z7\{0} which have no discrete logarithmswith base 2.(d) Find all nonzero elements of Z7\{0} which have no discrete logarithmswith base 3.

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Please do Exercise 16.1.6 part ABC and show step by step and explain Exercise 16.1.6.550CHAPTER 16 FURTHER TOPICS IN CRYPTOGRAPHY(a) We may define a function f : Z7\ {0} → Z7\ {0} by the equation:f(n)= mod(2,7). Use parts (a) and (b) of Exercise 16.1.5 to provethat f is neither one-to-one nor onto.(b) We may also define a function g: Z7\ {0} → Z7\ {0} by the equation:g(n)= mod (3, 7). Prove or disprove: g is one-to-one.(c) With the same g as in part (b), prove or disprove: g is onto. In previous math courses you learned that the inverse operation of expo-nentiation is taking the logarithm: for example, 23 = 8 while log₂ 8 = 3. Itis possible to do the same with discrete exponentiation: an inverse operationto discrete exponentiation is referred to as 'finding a discrete logarithmor (DL)'. Note that since discrete exponentiation involves raising to a powerwhich is a natural number, a DL will always be a natural number. For ex-ample, since mod (25, 7) = 4, we could say that under multiplication mod 7,5 is a DL of 4 with base 2.Now why have we been saying, &#34;a DL&#34; rather than &#34;the DL&#34;? Becausethere happens to be more than one:Exercise 16.1.5.(a) Find all natural numbers n such that mod (2&#34;, 7) = 4. Use your resultto complete the following sentence: &#34;Under multiplication mod 7, thediscrete logarithm(s) of 4 with base 2 are ....&#34;(b) Find all natural numbers n such that mod (2, 7) = 3. Use your resultto complete the following sentence: &#34;Under multiplication mod 7, thediscrete logarithm(s) of 3 with base 2 are ....&#34;(c) Find all nonzero elements of Z7\{0} which have no discrete logarithmswith base 2.(d) Find all nonzero elements of Z7\{0} which have no discrete logarithmswith base 3.

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