Discrete Mathematics: Propositional Logic. Section Summary. Propositions Logical Connectives Negation Conjunction Disjunction Implication; contrapositive , inverse, converse Biconditional Truth Tables. Propositions.
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“If you get 100% on the final, then you will get an A.”
if p, qponly if q: p cannot be T when q is not T
qwheneverppis sufficient for q
qfollows from pqis necessary for p
Getting %100 in the final exam is sufficient to get “A”.
To get “A”, it is necessary to get %100 in the final exam.
Example: Find the converse, inverse, and contrapositive of “It raining is a sufficient condition for my not going to town.”
converse: If I do not go to town, then it is raining.
contrapositive: If I go to town, then it is not raining.
inverse: If it is not raining, then I will go to town.
Example: Show using truth tables that neither the converse nor inverse of an implication are not equivalent to the implication.
Solution: 2n We will see how to do this in Chapter 6.
p q r is equivalent to(p q) r
If the intended meaning is p (q r )
then parentheses must be used.