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CIS 1910 > Logic > Flashcards

Flashcards in Logic Deck (30)
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1

logic

the study of formal reasoning

2

proposition

a statement that is either true or false, typically declarative sentences

3

truth value

indicating whether the proposition is actually true or false

4

compound proposition

created by connecting individual propositions with logical operators

5

logical operation

combines propositions using a particular composition rule

6

conjunction

/\, 'p and q', true if both p and q are true, false if one or both are false

7

truth table

shows truth value of a compound proposition for every possible combination of truth values for the variables

8

conjunction english examples

p and h, p but h, although p, h

9

disjunction

\/, 'p or q' 'p \/ q' true if either p or q or both are true, false if both are false

10

exclusive or (circle w/ plus)

evaluates to true when p is true and q is false, or vise versa

11

inclusive or

operates the same as disjunction

12

negation

reverses the truth value of the proposition

13

order of operations w/o parentheses

1. negation, 2. conjunction, 3. disjunction, 4. exclusive or, 5. conditional operation, 6. biconditional operation

14

how many rows will be in a truth table?

n variables = 2^n rows

15

conditional operation

->, reads if p then q, false if p is true and q is false, otherwise, true

16

p -> q, what is proposition p called?

hypothesis

17

p -> q, what is proposition q called?

conclusion

18

conditional operation english expressions

if p, then q; if p, q; q if p; p implies q

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converse of p -> q

q -> p

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contrapositive of p -> q

negation(q) -> negation(p)

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inverse of p -> q

negation(p) -> negation(q)

22

biconditional operation

p q, true when p and q have the same truth values and false when they do not

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biconditional operation english expressions

p if and only if q, p is necessary and sufficient for q

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iff

if and only if

25

tautology

when compound proposition is always true

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contradiction

when compound proposition is always false

27

showing that compound proposition is tautology

show set of truth values for its individual propositions that cause the compound to be true

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showing that compound proposition is contradiction

show set of truth values for its individual propositions that cause the compound to be false

29

logical equivalence

if they have the same truth value regardless of the truth values of their individual propositions (three lines)

30

de morgan's law

negation(p \/ q) l.e negation(p) /\ negation(q)