Flashcards in Module 1 Deck (44):

1

## What is a proposition?

### It is a declarative statement that must be EITHER true or false, not both.

2

## What is the negation operator and what does it do?

### ~, it turns a statement into it’s inverse. Ex: p = Tom is human. ~p = Tom is not human.

3

## What is the conjunction operator and what does it do?

### And (^). p^q is true if, and only if, p and q are both true.

4

## What is the disjunction operator and what does it do?

### Or, V, pVq is true if, and only if, p or q are true.

5

## What is the implication operator and what does it do?

### Arrow, p implies q. If p is true then q must be true. If p is false then q could be either true or false.

6

## What does p but q mean?

### p and q, p^q

7

## What does neither p nor q mean?

### Not p and not q, ~p^~q

8

## What is XOR derived from?

### P or q and not p and q, (pVq) ^ ~(p^q)

9

## What is the definition of a logical equivalence?

### When two statements have logically equivalent forms when identical component statement variables are used to replace identical component statements.

10

## What is De Morgan’s law of conjunction?

###
The negation of the conjunction of two statements is logically equivalent to the disjunction of their negations.

~(p^q) = ~p V ~q

11

## What is De Morgan’s law of disjunction?

###
The negation of the disjunction of two statements is logically equivalent to the conjunction of their negations.

~(pVq) = ~p ^ ~q

12

## What is a tautology?

### A statement form that is always true regardless of the truth values of the individual statements substituted for its statement variables.

13

## What is a contradiction?

### A statement form that is always false regardless of the truth values of the individual statements substituted for its statement variables.

14

## What is the commutative law of conjunction?

### p^q = q^p

15

## What is the commutative law of disjunction?

### pVq = qVp

16

## What is the associative law of conjunction?

### (p^q)^r = p^(q^r)

17

## What is the associative law of disjunction?

### (pVq)Vr = pV(qVr)

18

## What is the distributive law of conjunction?

### p^(qVr) = (p^q)V(p^r)

19

## What is the distributive law of disjunction?

### pV(q^r) = (pVq)^(pVr)

20

## What is the identity law of conjunction?

### p^t = p

21

## What is identity law of disjunction?

### pVc = p

22

## What is the negation law of disjunction?

### pV~p = t

23

## What is the negation law of conjunction?

### pVc = p

24

## What is the definition of the double negative law?

### ~(~p) = p

25

## What is the definition of the idempotent law of conjunction?

### p^p = p

26

## What is the idempotent law of disjunction?

### pVp = p

27

## What is the universal bound law of disjunction?

### pVt = t

28

## What is the universal bound law of conjunction?

### p^c = c

29

## What is the absorption law of conjunction?

### pV(p^q) = p

30

## What is the absorption law of disjunction?

### p^(pVq) = p

31

## What is the negation of t?

### c

32

## What is the negation of c?

### t

33

## What is the definition of a conditional statement?

### If p and q are statement variables, the conditional of q by p is “if p then q” or “p implies q.”

34

## What are p and q called in a conditional statement?

###
p = the hypothesis (or antecedent)

q = the conclusion (or consequent)

35

## What does it mean to be vacuously true or true by default?

### When a conditional statement is true by virtue of the fact that its hypothesis is false

36

## What is the negation of a conditional statement?

### If p then q is logically equivalent to p and not q

37

## What is the contrapositive of a conditional statement?

### If not q then not p

38

## What is the converse of a conditional statement?

### If q then p

39

## What is the inverse of a conditional statement?

### If not p then not q

40

## What is logically equivalent to a normal conditional statement?

### The contrapositive, or, not p or q

41

## What is logically equivalent to the converse of a conditional statement?

### The inverse

42

## What is a biconditional statement?

### It means p if, and only if, q. True when both p and q are true or they are both false.

43

## What is a sufficient condition?

### If p then q

44