Question
E ACTIVITY 1.5.3: Expand then reduce the proposition. Jump to level 1 Simplify (p(mp)) to pm 3. Select ba from (ab)(ba) belowShow me how (p(mp))
E ACTIVITY
1.5.3: Expand then reduce the proposition.
Jump to level 1
Simplify (p(mp)) to pm
3. Select ba from (ab)(ba) belowShow me how
(p(mp))
CANCEL LAW
Laws
Distributive
(ab)(ac)
a(bc)
(ab)(ac)
a(bc)
Commutative
ab
ba
ab
ba
De Morgan's
(ab)
ab
(ab)
ab
Conditional
ab
ab
ab
(ab)(ba)
Complement
aa
T
aa
F
T
F
F
T
Identity
aT
a
aF
a
Double negation
a
a
1
2
Check
Next
1
2
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Additional exercises
Exercise 1.5.1: Label the steps in a proof of logical equivalence.
infoAbout
Below are several proofs showing that two logical expressions are logically equivalent. Label the steps in each proof with the law used to obtain each proposition from the previous proposition. The first line in the proof does not have a label.
(a)
(p q) (q p) |
(p q) (q p) |
(q p) (q p) |
q (p p) |
q (p p) |
q F |
q |
(b)
(p q) (p q) |
(p q) (p q) |
(p q) (p q) |
(p q) (p q) |
p (q q) |
p T |
p |
(c)
r (r p) |
r (r p) |
r (r p) |
(r r) p |
r p |
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