Quarter 1 Test 1
Contains Variations of the words 'for every'.
Universal Statements
Tautology
A statement form that is always true regardless of the truth values of the Individual statements substituted for it's statement values.
Fallacy
An error in reasoning that results in an invalid argument.
Find the next three terms in each sequence.
23,14, 5, -4, -13, ....
-22, -31, -40
Permutation
Set of elements as an ordered selection of outcomes
List all the strings of length 3 over A that have exactly one b.
aab, aba, baa
Let p= "x<3," "q=3," and r ="4<x"
x<x<3
r ^ p
What argument form is
If P then Q
P
Therefore Q
Modus Ponens
Find the next three terms
13/6, 15/7, 17/8
19/9, 21/10, 23/11
Combination
Arrangement of individual elements (order is not important)
True or False
{2} e {1,2,3}
False
Logical Equivalence
It is two ways of saying the same thing.
EX. 6 is greater than 2, and 2 is less than 6.
Is the following argument invalid because of Converse or Inverse error.
If John and Carl sit next to each other then the classroom will be loud, The classroom is loud, Therfore John and Carl are siting next to each other.
Converse Error
9C7
(9/7), 9!/7!(9-7)! -> 9x8x7!/ 7! 2 -> 36
Possibility Tree
A system for keeping track of possibilities of situations in which events happen in order.
Does there exist _______ such that if n is divided by 4 the remainder is 1 and if _______?
a. an integer n; n is divided by 3 the remainder is 7
b. an integer n; n is divided by 7 the remainder is 3
b. an integer n; n is divided by 7 the remainder is 3
DeMorgan's Law
The negation of an "and" statement is logically equivalent to the "or" statement in which each component is negated.
A sequence of statements
An Argument
6!/4!5!
6x5!/4!5! -> 1/4
Multiplication Rule
Multiplying the number of possibilities each "step" has to count the total number of possible outcomes for a whole scenario has.
There is a positive integer that is less than or equal to every positive integer.
Existential Universal Statement
p V q
p: Firemen work hard
q: Firemen wear red suspenders
Firemen work hard or firemen wear red suspenders
Write the converse, inverse, and contrapositive of "If Al is Tom's cousin, then Jim is Tom's grandfather."
Converse- If Jim is Tom's grandfather, then Al is Tom's cousin.
Inverse- If Al is not Tom's cousin, then Jim is not Tom's grandfather.
Contrapositive- If Jim is not Tom's grandfather, then Al is not Tom's cousin.
15C2
(15/2), 15!/2!(15-2)! -> 105
Possibility Tree Example Problem
Team A and Team B are playing in a tournament How many ways can the tournament end if a team has to win three games total or two games in a row?