Exam 1 Flashcards
(36 cards)
1
Q
!(p ^ q)
A
!p v !q (De Morgan)
2
Q
conjecture of p and q
A
p ^ q
3
Q
p ^ T == p
A
Identity Laws
4
Q
p v F == P
A
Identity Laws
5
Q
p v T == T
A
Domination Laws
6
Q
p ^ F ==F
A
Domination Laws
7
Q
p v !p == T
A
Negation Laws
8
Q
p v p == p
A
Idempotent Laws
9
Q
p ^ p == p
A
Idempotent Laws
10
Q
!(!p) == p
A
Double Negation Laws
11
Q
p v q
A
!p -> q
12
Q
p v q == q v p
A
Commutative Laws
13
Q
p ^ q == q ^ p
A
Commutative Laws
14
Q
p ^ !p == F
A
Negation Laws
15
Q
(p v q) v r == p v (q v r)
A
Associative Laws
16
Q
p v (q ^ r) == (p v q) ^ (p v r)
A
Distributive Laws
17
Q
p v (p ^ q) == p
A
Absorption Laws
18
Q
p -> q
A
!p v q
19
Q
!(p v q)
A
!p ^ !q (De Morgan)
20
Q
p ^ q
A
!(p -> !q)
21
Q
!q ^ (p ->q) -> !p
A
Modus Tollens
22
Q
p -> q
A
!q -> !p
23
Q
!ExP(x)
A
Ax!P(x)
24
Q
!AxP(x)
A
Ex!P(x)
25
p ^ (p -> q) -> q
Modus Ponenss
26
((p->q) ^ (q->r ))-> (p->r)
Hypothetical syllogism
27
p->(p v q)
Addition
28
(p ^ q) -> P
Simplification
29
((p) ^ (q)) -> (p ^ q)
Conjunction
30
((p v q) ^ (!p v r)) -> (q v r)
Resolution
31
even integer
if there exists an integer k such tat n=2k
32
odd integer
if there exists an integer such that n = 2k + 1
33
perfect square
if there exists an integer p such that a=b^2
34
Proof by contradiction
p->q == !q -> !p show that contrapositive is true
35
rational number
if there exists an integers p and q with q != 0 such that r = p/q
36
irrational number
if a number can not be made via p/q
