# Truth table (dual)

• Suyash Singh
In summary, The duality principle states that when dualizing an expression, you replace 'and' with 'or' and 't (tautology)' with 'c(contradiction)'. This can be proved using truth tables.

What is dual?

## The Attempt at a Solution

Not on net. Meaning of dual i don't know and can't find.

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Suyash Singh said:

## Homework Statement

View attachment 226222
What is dual?

## The Attempt at a Solution

Not on net. Meaning of dual i don't know and can't 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.

baldbrain said:
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 ?

Guys, the OP has left the building

baldbrain
MidgetDwarf said:
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.