Lesson #1: Statements
The following sentence is an example of this: “I hate it when my computer crashes”.
What is an Atomic Statement?
T or F, a propositional variable can be both true and false.
What is False?
While not explicitly stated, this logical connective is the same for “but” as well as its primary meaning.
What is “And”?
According to Professor Warner, the most basic and tedious method of solving a compound statement is by creating a this to document every possible result.
What is a Truth Table?
A funny way to remember the Logical Equivalence symbol is that it looks like a “super” version of this.
What is an Equals Sign? (=)
If all truth assignments for a given compound/atomic statement are true then it is an example of a this.
What is Tautology?
The following sentence is an example of this: “Forza Horizon 5 is a great car racing simulator if and only if Matt Dammon can twerk”.
What is a Compound Statement?
Here is a cheeky trick for calculating the number of rows in a Truth table. Take this number and raise it to the power of the total # of propositional variables.
What is 2?
When performing a truth calculation for the “Implies” logical connective using q, p. This is the only truth assignment that results in a result of False.
What is q=T, p=F?
According to Professor Warner, a more streamlined method of evaluating truth is to plug in the assigned these for each propositional variable.
What are the Truth Assignments?
When using 2 of this logical connective on a single propositional variable, it is logically equivalent to the original propositional variable.
What is “Not”? [Law of Double Negation]
If a proven tautology is enclosed within a “Not” logical connective, it now becomes a this.
What is Contradiction?
This logical connective as stated by Professor Warner is the easiest yet hardest one because many people falsely assume its sentences to be atomic statements.
What is “Not”?
When defining propositional variables, if we do not want them to be understood as the same, we must use this word when describing them.
What is Distinct?
The illustration of this logical connective is akin to a Ray in mathematics.
What is “Implies” and or “If…Then”?
When dealing with two compound statements linked by an “inclusive or” logical connective. If one of the compound statements is true, the result of the combined compound statement is this automatically.
What is True?
The two formulas for negating a conjunction and negating a disjunction are referred to as this law.
What are De Morgan’s Laws?
If you are asked to prove that a given statement is a tautology or a contraction in this way, you should not use a truth table.
What is Directly?
When a sentence in logics identifies itself to be false, it is an example of this logics concept.
What is the Liar’s Paradox?
When performing a truth table design with 3 distinct propositional variables, the number of times when all 3 are true or 3 all false is this.
What is 2?
These 3 logical connectives we learned form a “Complete Triangle” because every logics problem can be written in terms of these connectives.
What are “And”, “Or”, and “Not”?
When drawing a truth table, you do not count duplicates of this as separate rows, but, you do count duplicates of this as separate rows. [ORDER MATTERS]
What are Propositional Variables and Logical Connectives?
For both the “and” , “or” logical connectives, swapping the order of the propositional variables while keeping the result the same is this law.
What are the Commutative Laws?
If two proven contradictions are connected with a “biconditional” logical connective, it now becomes a this.
What is a Tautology?
The logical connective “or” has two connotations in english. However, in logics, we often only use this one.
What is the “Inclusive Or”?
In class, Professor Warner usually uses these letters to denote up to 4 atomic statements within a logics problem. [name all of the 4]
What are P, Q, R, and S?
When you are presented with a logic problem when the result is true when one of the two statements are true, but false when both are true. It is an example of this logical connective.
What is the “Exclusive Or”?
When evaluating truth for an “Implies” logical connective, looking at it statistically, more often than not, the result will be this.
What is True?
This law has the most possible examples at 4 compared to the average number of 2 examples for the others.
What are the Identity Laws?
Statistically speaking, when looking at a compound statement with only “and” logical connectives, it is more likely to be a this.
What is a Contradiction?