Propositional Equivalences

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Propositional Equivalences Rosen 5th and 6th
Editions section 1.2
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I assume you know what follows
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Okay?
If not then please read appropriate section from
Rosen
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Material for examples class
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Using the laws of propositional equivalence prove
that is a tautology
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Let P(x,y) be a propositional function (i.e. a
predicate). Is the expression
a tautology?
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Let P(x,y) be a propositional function (i.e. a
predicate). Is the expression
a tautology?

• What does the expression mean?
• Whats the truth table for implication?
• And whats a tautology?
• So, now can I prove this?
• Go for it!

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Prove this
if (!(x gt 5 (x lt 5 y lt 3)) z
true else z false is the same as
z (x lt 5 y gt 3)
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• Whats the difference between
• and
• and

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• Can you think of a reason why we might use
• in place of
• in place of