Discrete Math: 1) use a truth table to show (p -> q\')\' V (q -> p\') is a tauto

Question

Discrete Math:

1) use a truth table to show (p -> q')' V (q -> p') is a tautology

2) Draw the parse tree of the expression: p V (q r) <-> (p q) V (p r)

6) Suppose that l, m and w respectively denote the propositions"LInux is good," "Mac OS is good". and "Windows is good". (A) translate "Windows is evil, linux is good and mac os is good" into propositional form. (B) Translate: "Windows is evil. moreover, linux is good, and mac OS is good." into propositional form. (C) Prove the statement "windows is evil. Moreover, linux is good or Mac OS is good." and "Windows is evil and linux is good, or Windows is evil and Mac OS is good." are equivalent.

9)b:john is a business major c: john is a computer science major m: john is a math major r: john will be rich s: john is smart

write each of the following as propostiions using only the five given variables: (A) john is a comp sci major and a math major. (B) john is a math major and not rich (C) If john is a smart business major, then john will be rich. (D) if john is a computer science major or a math major, and he is not a business major, then john is smart. (E) if john is a business major who is not smart, then john will not be rich.

11) A fire alarm contains two smoke detectors. If either of the smoke detector is activated, a sprinkler system is turned on. If both of the smoke detectors are activated, then the fire department is called. Design a logic circut for this fire alarm.

Explanation / Answer

1) Truth table:

hence it is a tautology.

p p' q q' p-->q' (p-->q')' q-->p' (p-->q')' (q-->p') T F T F F T F T T F F T T F T T F T T F T F T T F T F T T F T T

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