A common mistake students make when writing proofs is to start with the conclusion (the end) and end with the hypothesis (aka the beginning or the assumptions given in the question). While starting from the conclusion is a common technique to derive a proof in rough working, a formal proof should generally be written by starting with the assumptions and ending with the conclusion.

Consider the following problem and choose all the valid solutions from the options given below.

Define the relation on by if and only if there exists some such that . Show that is reflexive.

Before using a theorem or lemma, make sure you (carefully) check that all conditions of said theorem or lemma are actually satisfied.

Fermat's little Theorem states that "If is a prime number then for any integer , we have ".

Choose the correct statement from the statements below.

One mistake students sometimes make is the so-called `proof by example'. The proof by example refers to the situation where the statement is validated for some examples or cases rather than validating for the general case. 

Consider the following claim and explanation. Is the explanation valid?

Claim:

"If is a prime number then is also a prime number."

Explanation:

"The statement holds for . Therefore, the statement is true for all prime numbers , that is, if is prime then is also prime."