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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

Empty set minus A equal Empty Set

Ø − A = Ø