Notesale: Turn your study into money

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Propositional Logic-II
This is a sequel of handout 2
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An implication is logically equivalent to its contrapositive
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Example
If Shan saw frost on the car, he wore a coat
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Now, inverse, converse and contrapositive of this
statement are given as:

Symbolic Form
Natural Language Form

Inverse
Converse
Contrapositive
wf
¬f  ¬w
¬w ¬ f
If Shan did not see frost on If Shan wore a coat, he saw If Shan did not wear a coat, he
the car, he did not wear a frost on the car
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coat
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What follows is a brief justification of their
equivalences
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However, it does not say anything about truth value of q when p is
false
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Thus, it is logically
equivalent to p → q
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That is, the statement is false only in the case when q
is false and p is true
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Hence, this is logically equivalent to "if p then q"
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Hence, the statement "q unless ¬ p" is false only when p is true and q is
false, but it is true otherwise
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Biconditionals
Let p and q be propositions
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Biconditional
statements are also called bi-implications
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" Then p ↔ q is the statement "You can take the flight if and
only if you buy a ticket
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It is false when p and q have opposite truth values, that is, when
you do not buy a ticket, but you can take the flight (such as when you get a free trip) and when you buy a ticket and
cannot take the flight (such as when the airline bumps you)
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e
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‫یہ سنگ و خشت نہیں جو تری نگاہ میں ہے‬
)‫(اقبال‬

‫وہی جہاں ہے ترا جس کو تو کرے پیدا‬

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