# DeMorgans laws and rules of logic

#### jj0424

1. Homework Statement
(p -> q) has an unambiguous meaning both in logic and in natural language. The DeMorgans laws tell us what is meant by the negation of a conjunction or the negation of a disjunction, but what is the negation of a conditional such as p -> q? Use the rules of logic to produce a meaning for...[not(p -> q), and translate it into natural language using the statement, "If I go to McDonalds, then i will get a Big Mac."

2. Homework Equations

¬ ( p ˅ q ) <=> ( ¬p ˄ ¬ q )
¬ ( p ˄ q ) <=> ( ¬p ˅ ¬ q ) De Morgans laws

3. The Attempt at a Solution

( p  q ) => ( ¬ p ˅ q ) Implication
¬ ( p  q ) => ¬ ( ¬ p ˅ q ) Implication
¬ ( ¬ p ˅ q ) <=> ( p ˄ ¬ q ) De Morgans
Translation:
I went to McDonalds, but I did not get a Big Mac.

Im not sure if this is the right way to solve this problem does anyone know if this is right or wrong?

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#### csprof2000

That's right.

NOT("If I go to McD, then I get a Big Mac")
<=>
NOT("I don't go to McD" OR "I get a Big Mac")
<=>
NOT("I don't go to McD") AND NOT("I get a Big Mac")
<=>
"I go to McD" AND "I don't get a Big Mac"
<=>
"I go to McD and I don't get a Big Mac".

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