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franz32
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I hope someone can help me prove one of De Morgan's Law:
(A intersection B)' = A' U B'
(A intersection B)' = A' U B'
I can suggest a way to prove it, although I've never formally done any of this stuff so I don't know if this approach is "acceptable." Anyways, it's a proof by contradiction. Assume the equation were false. That would mean that there exists and element, x, such that it is not in (A' U B') but is in (A intersection B)'. Now, if it is not in (A' U B'), then it is not in A' and it is not in B' (if it were in either of those, it would be in A' U B'). So, if it is not in A', it is in A, and if it is not in B', it is in B. Therefore, this element, x, is in A and it is in B, so it is in (A intersection B). Therefore, it is not in (A intersection B)'. This contradicts, the assumption, therefore the equation must be right.franz32 said:I hope someone can help me prove one of De Morgan's Law:
(A intersection B)' = A' U B'
Gokul43201 said:Draw a Venn Diagram.
It becomes painfully obvious.
franz32 said:I hope someone can help me prove one of De Morgan's Law:
(A intersection B)' = A' U B'
1+1=1 said:doing a truth table would be difficult,
The best way is to use LaTeX. Click the quote button in post #5 to see how AKG did it. (tex tags will produce slightly larger output than itex tags). You will like the LaTeX codes \lnot,\lor and \land. There are lots of lists of LaTeX symbols online that you can find using Google. I also recommend that you use the preview button to check that everything looks OK before you submit your post.jonsina said:which font should i use so that i can type the symbols
De Morgan's Law is a set of two logical equivalences that describe the relationship between two statements connected by the logical operators "and" and "or". It states that the negation of a conjunction (and statement) is logically equivalent to the disjunction (or statement) of the negations of the individual statements.
Augustus De Morgan, a British mathematician, discovered De Morgan's Law in the 19th century. He was also a logician and made significant contributions to the fields of mathematics and philosophy.
De Morgan's Law is important in logic and mathematics because it allows us to simplify complex logical statements and proofs. It also helps us understand the relationship between negations, conjunctions, and disjunctions.
De Morgan's Law can be applied in various real-life situations, such as in computer programming, where it is used to simplify and optimize code. It can also be used in problem-solving and decision-making by breaking down complex statements into simpler, equivalent forms.
Yes, De Morgan's Law can be extended to any number of statements connected by "and" and "or" operators. It follows the same concept of negating the entire statement and switching the logical operator. For example, the negation of the statement "A or B or C" would be "not A and not B and not C".