For the following questions you must use the rules of logic (Don’t use truth tables) a) Show that (p harr q) and (not p harr not q ) are logically equivalent. b) Show that not ( p o+ q) and (p harr q) are logically equivalent.

permaneceerc 2021-02-19 Answered
For the following questions you must use the rules of logic (Don’t use truth tables)
a) Show that (pq) and (¬p¬q ) are logically equivalent.
b) Show that not ( pq) and (pq) are logically equivalent.
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Expert Answer

Brittany Patton
Answered 2021-02-20 Author has 100 answers
Definitions
pq(pq)(¬p¬q) (1)
p(pq)¬(pq) (2)
Double negation law: ¬(¬p)p
Commutative laws: pqqp,pqqp
De Morgan's laws: ¬(pq)¬p¬q,¬(pq)¬p¬q
a) (¬p¬q)
(¬p¬q)(¬(¬p)(¬(¬q))
(¬p¬q)(pq)
(pq)(¬p¬q)
pq
b) ¬(pq)
¬((pq)¬(pq)
(¬(pq))(¬(¬(pq)))
(¬(pq))v(pq)
((¬p)(¬q))(pq)
(pq)((¬p(¬q))
pq

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