need help with this discrete math question: Prove the given expression is a taut
ID: 3109279 • Letter: N
Question
need help with this discrete math question:
Prove the given expression is a tautology by arranging the compound proposition - rule of propositional logic pairs into a series so that for each pair, the compound proposition in that pair can be formed by applying the law of propositional logic in that pair to the compound proposition in the previous pair.
a) [¬p (p V q)] q
_________________ p F by negation law
_________________ (p ¬q) q by De Morgan's law
_________________ (¬p q) q by identity law
_________________ p (¬q q) by associative law
_________________ [¬p (p q)] q
_________________ [T (¬p q)] q by negation law
_________________ p T by negation law
_________________ [F (¬p q)] q by negation law
_________________ [(¬p p) (¬p q)] q by distributive law
¬(¬p q) q by logical equivalence
(¬p q) q by De Morgan's law
T by domination law
You will need to pick 9 options and pick them in order from the 12 options please.
Explanation / Answer
The following are the series of
1. [¬p (p V q)] q
2. [(¬p p) (¬p q)] q by distributive law
3. [F (¬p q)] q by negation law
4. (¬p q) q by identity law
5. ¬(¬p q) q by logical equivalence
6. (p ¬q) q by De Morgan's law
7. p (¬q q) by associative law
8. p T by negation law
9. T by domination law
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