math 1: logic ch 19

Question 1

a statement is a sentence for which it is meaningful to say

Answer 1

that it is true or false

Question 2

negation of a statement is the statement formed by putting the words… in front of the original statement

Answer 2

“it is not true that”

Question 3

the symbol… is used for negation

Answer 3

~

Question 4

a statement and its negation have opposite

Answer 4

truth values

Question 5

if p is true ~p is

Answer 5

false

Question 6

if p is false ~p is

Answer 6

true

Question 7

if a statement claims that all objects of a certain type have a particular property, the negation of that statement says that at least

Answer 7

one of those objects does not have the property

Question 8

if a statement claims that some object of a certain type has a particular property, the negation of that statement says that

Answer 8

none of those objects has the same property

Question 9

a conditional statement is a sentence of the form “if p, then q” where p and q are given statements this is written

Answer 9

p→q and is read “p implies q”

Question 10

the converse of p→q is

Answer 10

q→p (order of statements reversed)

Question 11

inverse of p→q is

Answer 11

~p→~q (original statements are negated)

Question 12

contrapositive of p→q is

Answer 12

~q→~p (order of statements reversed and statements negated)

Question 13

whether a conditional statement is true or false, its contrapositive always has the same

Answer 13

truth value

Question 14

a conditional statement is logically equivalent to its ….Either both statements are … or both are ….

Answer 14

contrapositive; true; false

Question 15

the converse and inverse of a conditional statement are ….. either both statements are … or both are…

Answer 15

logically equivalent; true; false