Question

Lemma is a proven statement used for proving another statement.
(a) True
(b) False

Answer 1

Hint: To understand Lemma, we will first define it. Then we will see some popular lemma and understand its uses. Thus, we can identify whether the Lemma is a proven statement used for proving another statement or not.

Complete step-by-step answer:
A lemma is a minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to proving a theorem. Very occasionally lemmas can take on a life of their own (Zorn’s lemma, Urysohn’s lemma, Burnside’s lemma, Sperner’s lemma).
One of the most common Lemma which is introduced to even students in lower standards is Euclid’s lemma, which captures the fundamental property of prime numbers. If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b.
a = pb + r, where r is a real number.
Thus, we conclude that according to the definition, Lemme is a proven statement used for proving another statement. As in some theorems, minor Lemmas are used to prove complex problems.
So, the correct answer is “Option A”.

Note: Lemmas are used very often in mathematics and can be seen in various proofs. It can often be confused with theorems. But theorems are defined as a mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results