"and so forth"
What is an elipsis?
The opposite truth value of a variable. "~"
What is negation?
If p then q
p
therefore q
What is Modus Ponens
Find the next three terms in each sequence:
23, 14, 5, -4, -13, ...
What is -22, -31, and -40?
Define the statement below:
All dogs are mammals.
Let A = {a, b}. List all strings of length 3 over A that have exactly one b.
What is (b, a, a), (a, b, a), (a, a, b)?
A statement that is true if either variable is true. "v"
What is disjunction?
The following argument is invalid because of a ____ error:
If a duck and a lemonade stand are in close proximity to each other, then the grapes will be inquired for.
The grapes were inquired for.
Therefore a duck and a lemonade stand are in close proximity to each other.
What is a converse error?
Simplify:
16!
13!4!
What is 140?
If two statements alligns with each other, being congruent.
What is logical equivalence?
State the following as true or false
2 ∈ {1, 2, 3}
{2} ∈ {1, 2, 3}
{2} ∈ {{1}, {2}}
True
False
True
The opposite of "and" is "or", and vice versa.
^--v
<-->
What is DeMorgan's Law?
Write the converse, inverse, and contrapositive of "If Wyatt disappears for two weeks or longer, then Wyatt is permanently gone."
What is "If Wyatt is permanently gone, then Wyatt disappears for two weeks or longer," "If Wyatt does not disappear for two weeks or longer, then Wyatt is not permanently gone," and "If Wyatt is not permanently gone, then Wyatt does not disappear for two weeks or longer?"
Evaluate the series:
What is 144 + 216 + 324 + 486 = 1170
if p then q
if q then r
therefore if p then r
What is transivity?
Let A = {a, b, c,} and B = {u, v}. List the amount of elements
A x B =
What is {(a, u), (a, v), (b, u), (b, v), (c, u), (c, v)} with 6 elements?
Write the statement in words if:
p: Wyatt is egocentric.
q: Wyatt wears hoodies.
The statement: ~(q V p)
What is "either Wyatt does not wear hoodies or Wyatt is not egocentric?"
Write a truth table for:
P -> ~q
q -> ~p
.'. p V q
What is
p q ~p ~q p->~q q->~p p V q
T T F F F F T
T F F T T T T
F T T F T T T
F F T T T T F
?
Evaluate the expression.
15C2
Hint: Use n!
r!(n-r)!
What is 105?
p or q
not p
therefore q
What is elimination?
Fill in the blanks to rewrite the following statement with variables:
"Is there an integer with a remainder of 4 when it is divided by 9 and a remainder of 2 when it is divided by 7?"
Hint: Is there an integer n such that n has _______?
What is "Is there an integer n such that n has a remainder of 4 when divided by 9 and a remainder of 2 when divided by 7?"
Compose a truth table for the statement form below and determine whether or not they are logically equivalent.
(p^q)^r and p^(q^r)
What is
p q r p^q q^r (p^q)^r p^(q^r)
T T T T T T T T
T T F T F F F F
T F T F F F F F
T F F F F F F
F T T F T F F
F T F F F F F
F F T F F F F
F F F F F F F
"Yes, they are logically equivalent?"
Determine whether the following argument 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.
What is
p q r pVq (pVq)->r rVq .'.pVq
T T T T T T T crucial valid
T T F T F T T
T F T T T T T crucial valid
T F F T F F T
F T T T T T T crucial valid
F T F T F T T
F F T F T T F crucial invalid
F F F F T F F
invalid, because line 7 is crucial, yet its conclusion is false?
Calculate each product(ignore question below):
What is 1*4*9*16*25 = 5,400?
Every real number has an additive inverse.
What is an universal existential statement?