Truth table (dual)

  • #1
Suyash Singh
168
1

Homework Statement


upload_2018-5-27_9-28-37.png

What is dual?

Homework Equations




The Attempt at a Solution


Not on net. Meaning of dual i dont know and cant find.
 

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Answers and Replies

  • #3
baldbrain
236
21

Homework Statement


View attachment 226222
What is dual?

Homework Equations




The Attempt at a Solution


Not on net. Meaning of dual i dont know and cant find.
In layman's terms, Duality principle just says that you replace each and every 'and' with 'or' & vice-versa; every 't (tautology)' with 'c(contradiction)'
So first you express 'p implies q' in an equivalent form of 'ands' and 'ors', same thing again with the whole expression, and then apply the dual.
Keep in mind that you don't touch the negations (if any) in the expression. For further reading, visit Boolean algebra - Wikipedia.
 
  • #4
MidgetDwarf
1,291
463
In layman's terms, Duality principle just says that you replace each and every 'and' with 'or' & vice-versa; every 't (tautology)' with 'c(contradiction)'
So first you express 'p implies q' in an equivalent form of 'ands' and 'ors', same thing again with the whole expression, and then apply the dual.
Keep in mind that you don't touch the negations (if any) in the expression. For further reading, visit Boolean algebra - Wikipedia.

Not sure If I understood correctly. Do we just take the contrapositive of this statement? It is the first time I hear the word dull.
or do you mean 'p implies q' is equivalent to not P ∨ Q ?
 
  • #5
phinds
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Guys, the OP has left the building
 
  • #6
baldbrain
236
21
Not sure If I understood correctly. Do we just take the contrapositive of this statement? It is the first time I hear the word dual.
or do you mean 'p implies q' is equivalent to not P ∨ Q ?
No, not contrapositive.
For a second, forget about duals & everything.
Using truth tables, prove that p→q ≡ ~p v q.
Then, just replace 'v' by '∧' without doing anything to the negation and without changing anything else. If, there's any t or c as I mentioned above, you interchange them as well.
 

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