Q1T1
True/False:
2 ∈ {1, 2, 3 }
True
DeMorgan's Law:
- 10 < x< 2
- 10 ≥ x or ≥ 2
p
therefore p or q
Generalization
Find the next three terms in the sequence:
3, 5/2, 7/3, 9/4, 11/5...
13/6, 15/7, 17/8
A sequence of statements:
(Q2T1)
Argument
Contain variations of the words 'for every'.
Universal Statements
DeMorgan's Law:
x < 2 or x > 5
x ≥ 2 and x ≤ 5
p or q
not p
therefore q
Elimination
Evaluate the series. Use a calculator:
5
∑ a (a+1)
a = 0
= 70
Assumptions or hypotheses of an argument:
(Q2T1)
Premises
True/False:
{2} ∈ {1, 2, 3}
False
Complete the truth table. Determine if it contains tautologies, contradictions, or neither.
(p ∧ q) ∨ ~p
Neither
What argument form is this?
If I wake up early, then I will take a shower.
I got up early, therefore I will take a shower.
Modus Ponens
Rewrite each series as a sum:
5
∑ m(m-2)
m = 1
= -1+0+3+8+15
Final statement of an argument
(Q2T1)
Conclusion
Contain versions of the word 'there is'
Existential Statements
Complete the truth table. Determine if it contains tautologies, contradictions, or neither.
(p ∨ q) ∧ (~p ∧ ~q)
Contradiction
What argument form is this?
If I eat good food, then I will be healthy.
I am not healthy, therefore I don't eat good food.
Modus Tollens
9C7
= 36
An error in reasoning that results in an invalid argument:
(Q2T1)
Fallacy
True/False:
{2} ∈ {{1}, {2}}
True
Complete the truth table for the statement forms below and determine whether or not they are logically equivalent.
(p ∧ q) ∧ r and p ∧ (q ∧ r)
Not logically equivalent
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
Simplify:
6!/4! 5!
= 6
If p then q
if q then r
therefore if p then r
(Q2T1)
Transitivity