Answer:
See the argument below
Step-by-step explanation:
I will give the argument in symbolic form, using rules of inference.
First, let's conclude c.
(1)⇒a by simplification of conjunction
a⇒¬(¬a) by double negation
¬(¬a)∧(2)⇒¬(¬c) by Modus tollens
¬(¬c)⇒c by double negation
Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.
An alternative approach to De Morgan's law is the following:
By contradiction proof, assume h is true.
h⇒d∨h by addition
(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.
