1) State the name of the law used in the identity: i. -(-p^q) V T=T ii. TV¬(¬p^q) =¬(¬p^q) V T, iii. ¬(¬p^ q) ^ T =¬(¬p^ ). iv. -(-p A q) = --p V ¬q.
1) State the name of the law used in the identity: i. -(-p^q) V T=T ii. TV¬(¬p^q) =¬(¬p^q) V T, iii. ¬(¬p^ q) ^ T =¬(¬p^ ). iv. -(-p A q) = --p V ¬q.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![HW1
Discrete Mathematics
1) State the name of the law used in the identity:
i.
¬(¬p^ q) V T = T
ii.
T V ¬(¬p^ q) =¬(-p^q) V T.
iii.
¬(¬p^ q) A T = ¬(¬p^ q).
iv.
¬(-p ^ q) = ¬-pV¬q
2) Without truth tables to show that [ ¬ (p A q) V (p A q) ] = T
3) Without truth tables to show that ¬ (p V (¬ p A q)) = ¬ (p V q)
4) Without truth tables to show that (¬p → q) =p V q.
5) Use truth tables to show that ¬ (p → q) = p ^¬q.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe31b72fe-051b-4353-b944-67fe9d203ad9%2Fa630ee80-9c03-41be-b8f8-28a3e57f7df9%2Fbcentib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:HW1
Discrete Mathematics
1) State the name of the law used in the identity:
i.
¬(¬p^ q) V T = T
ii.
T V ¬(¬p^ q) =¬(-p^q) V T.
iii.
¬(¬p^ q) A T = ¬(¬p^ q).
iv.
¬(-p ^ q) = ¬-pV¬q
2) Without truth tables to show that [ ¬ (p A q) V (p A q) ] = T
3) Without truth tables to show that ¬ (p V (¬ p A q)) = ¬ (p V q)
4) Without truth tables to show that (¬p → q) =p V q.
5) Use truth tables to show that ¬ (p → q) = p ^¬q.
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