Vocab
"p or q", denoted pvq
disjunction
a placeholder for unknown or general values
Variable
p or q
not p
therefore q
Elimination
rewrite the series as a sum
-1+0+3+8+15
write the statements in words if: p = Firemen work hard and q = firemen wear read suspenders
~ q
Firemen do not wear red suspenders
"not p", denoted
negation
contains versions of the words 'if-then'
conditional statements
assumptions or hypothesis of an argument
assumptions
rewrite the series as a sum
184+175+164+151
write the statements in words if: p = Firemen work hard and q = firemen wear read suspenders
p ^ q
Firemen work hard and wear red suspenders
a statement that is true or false but not both
Statement/Proposition
True/False. The sentence "is there an integer with a remainder of 1 when it is divided by 4 and a remainder of 3 when it is divided by 7" is equal to "is there an integer n such that n has a remainder of 1 when it is divided by 4 and a remainder of 3 when divided by 7"
True
is it Converse or Inverse error
if John and Carl sit next to each other, then the classroom will be loud
the classroom is loud
Therefore John and Carl are sitting next to each other
converse error
evaluate the series
126
write the statements in words if: p = Firemen work hard and q = firemen wear read suspenders
~ (q v p)
Firemen do not wear red suspenders and firemen do not work hard
statement is always true regardless of the truth values of the individual statements substituted for its statement values
Tautology
True/False The sentence "There is an integer n such that 1/n is also an integer" rewritten is "There is an integer whose additive inverse is also an integer."
False
if p then q
not q
therefore not p
Modus Tollens
evaluate the series
449
write the statements in words if: p = Firemen work hard and q = firemen wear read suspenders
p v q
Firemen work hard or firemen wear red suspenders
The negation of an "and statement" is logically equivalent to the "or statement" in which each component is negated and vice versa
DeMorgan's Law
Fill in the blank "Does there exist such that if n is divided by 4 the remainder is 1 and if ?
an integer; n is divided by 7 the remainder is 3
True or false The rewritten "if-then form" of "Getting an answer of 10 for problem 16 is a necessary condition for solving problem 16 correctly is "If someone does not get an answer of 16 for problem 10, then the person will not have solved problem 10 correctly
False
evaluate the expression
36
write the statement in symbolic form using ^ and V
Use: p = "x<3," q= "x=3," and r = "4<x"
4 < x < 3
r ^ p