Flashcards in Proof Deck (40):
1
Converse
P=>Q is Q=>P
2
P=>Q is Q=>P
Converse
3
Contrapositive
P=>Q is (~Q)=>(~P)
4
P=>Q is (~Q)=>(~P)
Contrapositive
5
DeMorgan's Law [~(P^Q)]
[~(P^Q)<=>(~P v ~Q)]
6
(~P v ~Q)] <=>
DeMorgan's Law [~(P^Q)]
7
DeMorgan's Law [~(PvQ)]
[~(PvQ) <=> (~P ^ ~Q)
8
(~P ^ ~Q) <=>
DeMorgan's Law [~(PvQ)]
9
P => Q equal to
~P v Q
10
~P v Q equal to
P => Q
11
P <=> Q equal to
(P => Q) ^ (Q => P)
12
(P => Q) ^ (Q => P) equal to
P <=> Q
13
~( P => Q) equal to
(P ^ ~Q)
14
(P ^ ~Q) equal to
~( P => Q)
15
~(P ^ Q) equal to
P => ~Q and Q => ~ P
16
P => ~Q and Q => ~ P ---equal to
~(P ^ Q)
17
P =>(Q => R) equal to
(P^Q) => R
18
(P^Q) => R ---equal to
P =>(Q => R)
19
P =>(Q ^ R) equal to
(P=>Q) ^ (P=>R)
20
(P=>Q) ^ (P=>R) -- equal to
P =>(Q ^ R)
21
(P v Q) => R equal to
(P=>R) ^ (Q=>R)
22
(P=>R) ^ (Q=>R) equal to
(P v Q) => R
23
A − B = {x: x ∈ A and x ∉ B}.
For x, such that X is within A and not within B
24
For x, such that X is within A and not within B
A − B = {x: x ∈ A and x ∉ B}.
25
A ∩ B = {x: x ∈ A and x ∈ B}.
For x, such that x is within A and B
26
For x, such that x is within A and B
A ∩ B = {x: x ∈ A and x ∈ B}.
27
A ∪ B = {x: x ∈ A or x ∈ B}.
For x, such that x is within A or B or Both
28
For x, such that x is within A or B or Both
A ∪ B = {x: x ∈ A or x ∈ B}.
29
A ⊆ A ∪ B
A is a subset of A or B
30
A is a subset of A or B
A ⊆ A ∪ B
31
A ∩ B ⊆ A.
A and B are a subset of A
32
A and B are a subset of A
A ∩ B ⊆ A.
33
A ∩ Ø = Ø
A and Empty set equal Empty Set
34
A and Empty set equal Empty Set
A ∩ Ø = Ø
35
A ∪ Ø = A.
A or Empty Set equal A
36
A or Empty Set equal A
A ∪ Ø = A.
37
A − Ø =A
A minus Empty set equal A
38
A minus Empty set equal A
A − Ø =A
39
Ø − A = Ø
Empty set minus A equal Empty Set
40