) Show that¬(p∨(¬p∧q))≡¬p∧¬q . Please show each step and the laws you use. 2) Show that¬(p∨¬q)∨(¬p∧¬q)≡¬p. Please show each step and the laws you use. Example: (p∧q)→p ≡¬(p∧q)∨p [Identity of implies] ≡(¬p∨¬q)∨p [De Morgan’s law] ≡(¬p∨p)∨¬q [Associative law] ≡T∨¬q [Negation law] ≡T [Domination law]
) Show that¬(p∨(¬p∧q))≡¬p∧¬q . Please show each step and the laws you use. 2) Show that¬(p∨¬q)∨(¬p∧¬q)≡¬p. Please show each step and the laws you use. Example: (p∧q)→p ≡¬(p∧q)∨p [Identity of implies] ≡(¬p∨¬q)∨p [De Morgan’s law] ≡(¬p∨p)∨¬q [Associative law] ≡T∨¬q [Negation law] ≡T [Domination law]
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 16CT: Let P represent any statement. Classify as true or false. a P and P b P or P
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Question
1) Show that¬(p∨(¬p∧q))≡¬p∧¬q . Please show each step and the laws you use.
2) Show that¬(p∨¬q)∨(¬p∧¬q)≡¬p. Please show each step and the laws you use.
Example:
(p∧q)→p
≡¬(p∧q)∨p [Identity of implies]
≡(¬p∨¬q)∨p [De Morgan’s law]
≡(¬p∨p)∨¬q [Associative law]
≡T∨¬q [Negation law]
≡T [Domination law]
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