Proving De Morgan's Law Without Truth Tables: ~(~p∧~q) = ~p∨~q

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In summary, the conversation is about proving the equivalency between ~(p^q) and ~pv~q without using truth tables. The suggestion is to use natural deduction and refer to a specific example in a textbook. The conversation also mentions confusion about two specific rules and the need to prove a different version of de Morgan's law.
  • #1
poutsos.A
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Hi ,my lecturer ask me to prove ~(p^q) = ~pv~q i.e ~(p^q) is equivalent to ~pv~q,without using the true tables.

thanks for your help
 
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  • #2
What have you tried? You should have some basic instructions for working with statements like this.
 
  • #3
the usual in statement calculus. i can not get started
 
  • #5
thanks,but where rules 7 and 13 are coming from what are they called?

also my version of de morgan is not proved there, probably that's why the lecturer ask me to prove that version because he knew the one already in google
 

What is de Morgan's law?

De Morgan's law is a fundamental principle in Boolean algebra that states that the negation of a disjunction is equivalent to the conjunction of the negations of the individual terms.

What are the two forms of de Morgan's law?

The two forms of de Morgan's law are the AND form, which states that the negation of a conjunction is equivalent to the disjunction of the negations of the individual terms, and the OR form, which states that the negation of a disjunction is equivalent to the conjunction of the negations of the individual terms.

How is de Morgan's law used in logic and computer science?

De Morgan's law is used to simplify logical expressions and to prove logical equivalences. It is also used in computer science to optimize digital circuits and in programming to manipulate Boolean expressions.

Can you provide an example of de Morgan's law in action?

Sure, for example, the statement "It is not raining or it is not sunny" can be rewritten as "It is not raining and it is not sunny" using de Morgan's law. This shows that the two statements are logically equivalent.

What is the significance of de Morgan's law in mathematics?

De Morgan's law is a fundamental tool in mathematical logic and is used to transform complex logical statements into simpler forms. It is also important in set theory, where it is used to simplify set operations and prove set identities.

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