Q1T1
Contain variations of the words "for every".
Universal Statement
Determine whether the follwing arguemnt is valid or invalid. Include a truth table and a few words explaining why the truth table shows validity or invalidity.
If Hugo is a physics major or if Hugo is a math major, then he needs to take calculus. Hugo needs to take calculus or Hugo is a math major. Therefore, Hugo is a physics major or Hugo is a math major.
(go to Google Doc for the table).
This is invalid because row #7 has 2 true premises and 1 false conclusion which makes it automatically invalid.
Find the next three terms in the sequence.
23, 14, 5, -4, -13
-22, -31, -40
Write the statement in words if:
p: Firemen work hard
q: Firemen wear read suspenders
~(q V p)
Firemen do not wear red suspenders and firemen work hard.
Write symbolic form using V and ^.
Let p= "x< 3", q= "x=3", and r= "4< x"
x ≤ 3
p V q
contain versions of the words "if- then".
Conditional Statement.
p or q
not p
therefore q
Elimination
16!/ 13!4!
140
Define the term and give a specific example for the term.
Statement/ Proposition:
Thisis a sentence that is true or false but not both.
Example: Grass is green.
if p then q
if q then r
therefore if p then r
Transitivity
Is there an integer with a remainder of 1 when it is divided by 4 and remainder of 3 when it is divided by 7.
Does there exist _____ such that if n is divided by 4 the remainder is 1 and if _____?
an integer n; n is divided by 7 the remainder is 3.
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. Therefore John and Carl are sitting next to each other.
Converse error
Rewrite this series as a sum.
5
Σ m(m-2)
m=1
-1+0+3+8+15
m1= 1(1-2)= -1
m2= 2(2-2)= 0
m3= 3(3-2)= 3
m4= 4(4-2)= 8
m5= 5(5-2)= 15
Define the term and give an example.
DeMorgan's Law.
The negation of an "and" statement is logically equivalent to the "or" statement in which each component is negated. The same goes for an "or" statement.
Example: John is 6 feet tall and he weight at least 200 lbs.
John is not 6 feet tall or he weighs less than 200 lbs.
"and so forth"
Elipsis
Let A= {a,b}. List all the strings of length 3 over A that have exactly one b.
1. a,a,b
2. b,a,a
3. a,b,a
An error in reasoning that results in an invalid argument.
Fallacy
Evaluate this series, use a calculator
5
Σ (50-m)
m=1
235
calculator: Math then summation
Complete the truth table and determine if it's a tautology, contradiction, or neither.
(p v q) ^ (~p ^ ~q)
Contradiction.
See Google Doc.
{1,2,3}
Set Roster Notation
Let A= {a,b,c} and B= {u,v}.
A x B=
{(a,u), (a,v), (b,u), (b,v), (c,u), (c,v)}
If p then q
p
therefore q
Modus Ponens
Evaluate each expression. n!/r!(n-r)!
9 C 7
36
Complete the truth table and determine if it's a tautology, contradiction, or neither.
(p ^ q) v ~p
Neither.
See Google Doc
Every real number has an additive inverse.
Universal Existential Statement