Logic

Question 1

logic

Answer 1

the study of formal reasoning

Question 2

proposition

Answer 2

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

Question 3

truth value

Answer 3

indicating whether the proposition is actually true or false

Question 4

compound proposition

Answer 4

created by connecting individual propositions with logical operators

Question 5

logical operation

Answer 5

combines propositions using a particular composition rule

Question 6

conjunction

Answer 6

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

Question 7

truth table

Answer 7

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

Question 8

conjunction english examples

Answer 8

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

Question 9

disjunction

Answer 9

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

Question 10

exclusive or (circle w/ plus)

Answer 10

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

Question 11

inclusive or

Answer 11

operates the same as disjunction

Question 12

negation

Answer 12

reverses the truth value of the proposition

Question 13

order of operations w/o parentheses

Answer 13

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

Question 14

how many rows will be in a truth table?

Answer 14

n variables = 2^n rows

Question 15

conditional operation

Answer 15

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

Question 16

p -> q, what is proposition p called?

Answer 16

hypothesis

Question 17

p -> q, what is proposition q called?

Answer 17

conclusion

Question 18

conditional operation english expressions

Answer 18

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

Question 19

converse of p -> q

Answer 19

q -> p

Question 20

contrapositive of p -> q

Answer 20

negation(q) -> negation(p)

Question 21

inverse of p -> q

Answer 21

negation(p) -> negation(q)

Question 22

biconditional operation

Answer 22

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

Question 23

biconditional operation english expressions

Answer 23

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

Question 24

iff

Answer 24

if and only if

Question 25

tautology

Answer 25

when compound proposition is always true

Question 26

contradiction

Answer 26

when compound proposition is always false

Question 27

showing that compound proposition is tautology

Answer 27

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

Question 28

showing that compound proposition is contradiction

Answer 28

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

Question 29

logical equivalence

Answer 29

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

Question 30

de morgan's law

Answer 30

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