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###### Vijay posted an Question
October 15, 2021 • 08:54 am 30 points
• IIT JAM
• Mathematics (MA)

## Own. please send the solution to the problem given in the attachment.

own. please send the solution to the problem given in the attachment.

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• ##### Navdeep goyal 1

Lemma is generally used to describe a "helper" fact that is used in the proof of a more significant result. Significant results are frequently called theorems. Short, easy results of theorems are called corollaries.

• ##### Deepak singh 1 Best Answer

1. Proposition is a mathematical statement that is either true or false. E.g. both ‘3 is greater than 4’ and ‘7 is prime’ are propositions, despite the fact that the first statement is false. 2. Theorem is a proven proposition. E.g. Pythagoras Theorem, stating for every right triangle with leg lengths a and b , and hypotenuse c , then the relation a2+b2=c2 always holds true. 3. corollary is a result from a theorem that doesn’t require too much proof to show. An example of this can be seen here: 4. Theorem: A triangle is isosceles iff two angles in a triangle are congruent. 5. Corollary: An equilateral triangle is equiangular. 6. A lemma is a theorem that is proven in a proof to help derive the next result. An example of this is below: Lemma: If prime p divides integer ab , then p divides a or p divides b .

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