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During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Proof Review, Proof Methods, Logical Equivalences, Set Equivalences, Truth Tables, Rules of Inference, Uniqueness Proofs, Combinatorial Proofs, Definition of Implication, Demorgan’s Law, Idempotent Law, Set Identities
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Idempotent Law
Associativity of Or
(¬ p ∨ r )∨(¬ q ∨ r )≡(¬ p ∨¬ q )∨ r
Definition of implication
Re-arranging
Original statement
DeMorgan’s Law
Proof by using basic set identities
Proof by showing each set
is a subset of the other 1
Proof by showing each set
is a subset of the other 2
p q
q
p
q
p
p q
p r
q r
p q
p q p r q r
r
p c
p
q r
p r
p q
=
n
k
n k
n
0
=
−
n
k
k n k k
n
0
2 n^ =( 1 + 1 )^ n
=
n
k k
n
0
=
−
n
j
n (^) xn jyj j
n x y 0
=
n
k
n k
n
0
n n
k k
n 2 0
=
0 n
=
n
k k
n
0
1 n
n n