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Byeonggon Lee
- 14
- 2
Hi I am studying mathematical logic by a pdf file. But there is no proof about this therorem so I don't understand.. How to prove this?
Truth table aha! thanksWWGD said:
The statement "(p ⇒ q) =(¬p ∨ q) proof" is a logical expression that represents a proof technique known as the law of contrapositive. It states that if p implies q, then the negation of p must imply the negation of q. In other words, if p is true, then q must also be true, and if p is false, then q must also be false.
The law of contrapositive is used in a proof by showing that if the negation of the conclusion is true, then the negation of the premise must also be true. This can be done by assuming the negation of the conclusion, and then using logical steps to show that the negation of the premise must also be true. This ultimately proves that the original statement is valid.
The steps involved in a "(p ⇒ q) =(¬p ∨ q) proof" are as follows:
No, the law of contrapositive can only be used to prove statements that are in the form of "p ⇒ q" (if p then q). It cannot be used to prove statements that are not in this form, such as "p ∧ q" (p and q) or "p ∨ q" (p or q).
Yes, the law of contrapositive is just one of many proof techniques in logic. Other techniques include proof by contradiction, proof by cases, and proof by mathematical induction. These techniques all involve using logical steps to show that a statement is true or false.