Q1T1
Rewrite the following statement without using variables:
There is an integer n such that 1/n is also an integer.
There is an integer whose reciprocal is also an integer.
What is a conjunction?
p∧q. The statement is only true when and only when both p and q are true. If either p or q is false, p∧q is false.
Write the converse, inverse, and contrapositive of the following statement:
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.
Find the next three terms in each sequence:
23, 14, 5, -4, -13
-22, -31, -40
Rule: -9
Turn this unless statement into a conditional statement:
We are going to the party unless it snows.
If it doesn't snow, then we are going to the party.
Write true or false for the following statement:
{2} ∈ {{1}, {2}}
True.
Remember: ∈ means the whole thing.
⊆ means to break it down.
Write the statement using the following words:
p: Firemen work hard.
q. Firemen wear red suspenders.
∼(q ∨ p)
∼q ∧ ∼p
Firemen do not wear red suspenders and Firemen do not work hard.
Is this argument invalid because of converse or inverse error?
If John and Carl sit next to each other, then the classroom with be loud.
The classroom is loud.
Therefore John and Carl are sitting next to each other.
Converse error.
If p then q
q
Therefore p
Rewrite each series as a sum:
5
∑ m(m-2)
m=1
-1 + 0 + 3 + 8 + 15
What is the argument type?
p or q
not p
therefore q
Elimination Rule
Let A = {a,b,c} and B= {u,v}
A X B
Answer in Google Doc
What is the difference between a tautology and a contradiction?
A tautology is a statement that is always true regardless of the truth values of the individual statements substituted for its statement variables.
A contradiction is a statement that is always false regardless of the truth values of the individual statements substituted for its statement variables.
Construct a table based on the argument form below and state if it is valid or invalid.
p→∼q
q→∼p
∴ p ∨ q
On Google Doc.
Evaluate this expression:
9 C 7
36
Rule: __n!__
r! (n-r)!
What is a permutation?
A set of elements as an ordered selection of outcomes.
Let A = {1,2,3,4} and B = {a,b,c} Define a function G: A --> B as follows: G= {(1,b), (2,c), (3,b), (4,c)}.
A. Find G(2)
B. Draw an arrow diagram for G.
A. G(2) = C
B. Google Doc
Using DeMorgan's Law write the negations for the statements.
-10 ≺ x ≺ 2
-10 ≺ x and x ≺ 2
Final answer below:
-10 ≥ x or x ≥ 2
Rewrite the following statement without using the word "necessary":
Getting an answer of 10 for problem 16 is a necessary condition for solving problem 16 correctly.
If someone does not get an answer of 10 for problem 16, then the person will not have solved problem 16 correctly.
Calculate the following product:
9
∏ 3^x
x=6
729 x 2187 x 6561 x 19683 = 2.05 x 10^14
What is a combination?
An arrangement of individual elements (order is not important).
Write the type of form this statement is in:
For every animal a, if a is a dog, then a is a mammal.
Universal Conditional Statement.
Draw a truth table for the following equation:
(p ∧ q) ∧ r and p ∧ (q ∧ r)
On Google Doc
Determine if the following argument is valid or invalid; include a truth table.
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.
On Google Doc.
__(n-3)!__
n!
_(n-3) (n-2) (n-1)!_
(n-1)!
___1____ ____1_____
n(n^2 - 3n + 2) = n^3 - 3n^2 + 2n
What is a possibility tree?
A system for keeping track of possibilities of situations in which events happen in order.