) 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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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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