Grammar[br]Proofs are written in complete sentences, using proper symbols, punctuation and grammar. [br]Conceptually, we also need to follow the [url=https://calcworkshop.com/logic/rules-inference/]rules of inference[/url] and use definitions, axioms, and theorems precisely.[br]Structure[br]All proofs can be divided into three parts: beginning, middle, and end.[br]The beginning is where we place statements assumed[i] to be true[/i] .[br]The middle of our proof is where we [i]include a series of logical statements l[/i]eading the reader to the end.[br]The “end” is where we conclude that[i] the statement is proved to be true. [/i]Also, it should be ended with 'QED', a Latin abbreviation meaning “that which was to be shown”.[br]There are two major groups of method in building a proof:[br][list=1][*]Direct Proofs.[/*][*]Indirect Proofs.[/*][/list]Direct proofs assume that a hypothesis is true and then develop a series of logically deductions to reach a conclusion.[br]In contrast, an indirect proof has two forms:[br][list=1][*]Proof By Contraposition.[/*][*]Proof By Contradiction.[/*][/list]For both of these scenarios, we start with the negation of the conclusion and prove either the hypothesis’s negation or a contradictory statement.