Chapter 1: Q3E (page 12)
What is the negation of each of these propositions?
a) Mei has an MP3 player.
b) There is no pollution in New Jersey.
c)
d) The summer in Maine is hot and sunny
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Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the outputfrom input bitsand p,q,r
Use a truth table to verify the first De Morgan law.
Find a compound proposition involving the propositional variables \(p,q\) and \(r\) that is true when \(p\) and \(q\) are true and \(r\) is false, but is false otherwise. (Hint: Use a conjunction of each propositional variable or its negation.)
Find the dual of each of these compound propositions..
a)
b)
c)
Show that, and,∨form a functionally complete collection of logical operators. [Hint: Use the fact that every compound proposition is logically equivalent to one in disjunctive normal form, as shown in Exercise 42.]
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