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Sets
Proofs
De Morgan's Laws
Rules of Inference 1
Rules of Inference 2
100
A = {2,4,6,8} B = {4,8,12,16} C = {2,4,6,8,12,16}
What is AUB?
100
If we are proving p→ q, then we will assume ¬q^ p
What is Proof By Contradiction?
100
∀x∃y ¬P(x)
What is ¬∃x∀y P(x) ?
100
p→q ¬q ∴¬p
What is Modus Tollens?
100
pVq ¬p ∴ q
What is Disjunctive Syllogism?
200
A = {2,4,6,8} B = {4,8,12,16} D = {4,8}
What is A∩B?
200
If we are proving p→ q, then prove ¬q→¬p
What is proof by contrapositive?
200
¬q = n is odd
What is the negation of q when q = n is even?
200
p→q q→r ∴ p→r
What is Hypothetical Syllogism?
200
P ∴pVq
What is Addition?
300
A = {2,4,6,8} X = 4
What is |A|?
300
∀x(x > 5)
What is Proof By Counter Example?
300
∃x(x≠7)
What is ¬∀x (x=7)?
300
p→q p ∴ q
What is Modus Ponens?
300
p q ∴ p^q
What is Conjunction?
400
D = {4,8,10} F = 2^3=8
What is |P(D)|?
400
∃x(x+1 > 2)
What is Existence Proof, or Proving by finding an example?
400
∀x(x≤10)
What is ¬∃x(x>10)
400
Prove Using ROI: p^q ∴pVq
p^q ∴p ----------By Simplification p ∴pVq-------By Addition
400
p^q ∴p
What is Simplification?
500

D = {4,8} X = {{},{4},{8},{4,8}}

What is P(D)?

500
If m and n are integers, prove that if m and n are perfect cubes then m * n is a perfect cube.
Direct Proof
500
(p^¬q)
What is ¬(p→q)?
500
Prove using ROI: p^q p→r r→s ∴s
p^q ∴p---------------Simplification p→r r→s ∴p→s-------------------HS p→s p ∴s-------MP
500
Prove using ROI a→b b→c c→d ∴a→d
a→b b→c ∴a→c------------By HS a→c c→d ∴a→d------By HS