Zero-Knowledge Proofs are used to prove that you do not know anything Select one: True O False

c) What is the inductive hypothesis of a proof that P(n) is true for all positive integers n? d) What do you need to prove in the inductive step of a de proof that P(n) is true for all positive integers n? e) Complete the inductive step of a proof that P(n) is true for all positive integers n, identifying where you use the inductive hypothesis.

Can you do this Java program please

Can someone help me solve this problems(Q1-Q6)? Mathematical Foundations of Computing Problems 1. Write each of the following conditional statements and the corresponding converse, inverse, and contrapositive as English sentences in the form “if ?, then ?.”Example: Whenever it rains, it pours.Answer:Original statement: If it rains, then it pours.Converse: If it pours, then it rains.Inverse: If it doesn’t rain, then it doesn’t pour.Contrapositive: If it doesn’t pour, then it doesn’t rain.1.1 You can do it if you put your mind to it.1.2 Being cold implies that you need a jacket.1.3 Petting the cat is sufficient for it to purr. 2. Determine the truth value of each of the following statements if the domain consists of all integers. If it is true, find a different domain for which it is false. If it is false, find a different domain for which it is true. Justify your answers.Example: ∀?(? ≤ ??)Answer:False. If ? = −1, then 2? = −2 and −1 > −2.True when the domain consists of all…