Propositional Logic

[匿名]

2013-10-26 9:10 pm

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Identify whether the following formula is a tautology, a contradiction
or contingent by producing its truth table. Then use the tautologies in
the tutorial notes or lecture notes to simplify the formula. If the
formula is a tautology or contradiction reduce it to T or F,
respectively. If the formula is contingent, derive the smallest
equivalent expression that uses conjunction, disjunction and negation
only. At each step in your proof use just one of the tautologies and
state which one was used.

(p⇔p)⇔(p⇒p)

回答 (1)

myisland8132

2013-10-27 5:38 am

✔ 最佳答案

So, when p is T, the formula becomes

(p⇔p)⇔(p⇒p)

(T⇔T)⇔(T⇒T)

T⇔T

T

when p is F, the formula becomes

(p⇔p)⇔(p⇒p)

(F⇔F)⇔(F⇒F)

T⇔T

T

So, the formula is a tautology

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