1.1 Deductive Reasoning and Logical Connectives Flashcards
What is a conclusion and a premise?
We arrive at a conclusion from the assumption that some other statements, called premises, are true.
In the example below, what are the premises and what is the conclusion?
It will either rain or snow tomorrow.
It’s too warm for snow.
Therefore is will rain.
The first two statements are the premises. The last statement is the conclusion.
What is a valid argument?
An argument is valid if the premises cannot all be true without the conclusion being true as well.
What is deductive reasoning and why is it important?
Deductive reasoning, is the process of reasoning from one or more statements (premises) to reach a logical conclusion.
The standard that’s used to judge the correctness of deductive reasoning is when there’s a sense that the conclusion is forced on us by the premises.
Deductive reasoning is important because it is the foundation for which to base a proof on.
What two advantages does replacing certain statements in the arguments give us?
- Keeps us from being distracted by aspects of the argument that don’t affect their validity.
- Highlights the usage of key words that have important in determining if an argument is valid.
∨ : meaning and name
Means “or” and is called a disjunction.
∧ : meaning and name.
Means “and” and known as conjunction.
¬ : meaning and name
Means “not” and is called negation.
When we don’t include a parenthesis in front of ¬, what arguments are negated? For example, what is negated in ¬P ∧ Q?
Only the statement immediately after the negation symbol is affected.
¬P ∧ Q = (¬P) ∧ Q
What word is used to represent parenthesis in logical statements?
For example:
S = John is stupid
L = John is lazy
What does ~S^(LvS) mean?
John isn’t stupid , and either he’s lazy or he’s stupid
What is a well-formed formula?
A well formed formula is one where all logical symbols are between statements or in the case of negation, only used before a statement.
Logical statements might not use the words or, and, not. An example is “but” to mean “and” between two contrasting statements.
Mathematical notation can have logical words as well. How to express 3 <= pi in logic?
P = 3 < pi
Q = 3 = pi
3 <= pi = P v Q
Or (3 < pi) v (3 = pi)
What is a logical connective and why is it important?
A logical connective is a word that connects multiple statements to form more complex statements.
They are important because they are usually the most important words in a logical argument in determining whether the reasoning is valid or invalid.
Analyze the logical form of the following statement:
We’ll have either a reading assignment or homework problems, but we won’t have both homework problems and a test.
(R v H) ^ ~(H ^ T), where
R = We’ll have a reading assignment
H = We’ll have homework problems
T = We’ll have a test
Uncommon words that are logical connectives:
Either
Neither
But
Either : ()
Neither : ~(A v B)
But : and
