Symbolic
Language
Language
This is is the name of a statement that does not contain any other statement as a component.
What is a simple statement?
This function flips the truth value from true to false and from false to true.
What is negation?
The truth table for a propositional schema should contain 2n rows, where 2 represents the two truth values—True and False—and n is this.
What is the number of propositional variables?
This rule of inference says:
if p then q
p
:. q
What is modus ponens?
This rule allows you to introduce or remove the disjunction or conjunction of a term with itself.
What is a tautology?
A truth-functional proposition whose component statements are connected by the truth-functional operator ‘and’ is called this.
What is a conjunction?
This relationship is usually expressed by the English phrase “if…then…” It is symbolically represented with a horseshoe.
What is material implication (or conditional)?
After we have determined how many rows we will be working with we start grouping our T’s and F’s on the table, beginning with the maximum number that we group together first. So, if our variables were 3 in number, we know it would be this.
What is 23 =8?
This rule allows you to bring two lines of an argument together.
What is conjunction?
Rule that allows you to reverse the positions of conjuncts or disjuncts.
What is commutation?
This rule is formed with two statements in English by inserting the word “or” between them.
What is disjunction?
The only time the conditional is false is when the antecedent is true and this is false.
What is the consequent?
Number of parenthesis units shown here:
[p v (q . r)]
What is a double parenthesis unit?
This is a sequence of statements—each of which is either a premise of a given argument or is deduced using the rules of inference from preceding statements in that sequence. The last statement in the sequence is the conclusion of the argument whose validity is being proved.
What is a formal proof of validity?
Rule that tells you if you are given a statement of the form ~ (p v q), you can replace it with the logically equivalent statement ~p · ~q.
What is DeMorgan's Theorem.
This rule states: if both are true, the entire function itself is true, otherwise it is false.
What is the rule for conjunction?
Essentially, this is just the conjunction of the conditions: if p then q and if q then p.
What is Material Equivalence?
The top of a truth table demonstrating an argument shows the variables, premises, and this.
What is the conclusion?
This rule of inference consists only of conditionals.
What is hypothetical syllogism?
“If you bother me (p) then I’ll punch you in the nose (q)” is logically equivalent to the statement: “Either you stop bothering me or I’ll punch you in the nose” through this rule of replacement.
What is material implication?
This truth-functional operator is true iff the first is true and the second is false, or the first is false and the second is true or both are true. The function is false only when all are false.
What is disjunction?
This symbolic logic ~(p v q) is the expression “neither p nor q.”
This ~p v q is expressed as ___________
What is “either not p or q”?
In a truth-table, validity is determined by looking to see if a row exhibits all these as true and the conclusion as false.
What are the premises?
This rule is illustrated like this:
(p -> q) · (r -> s)
p v r
:. q v s
What is constructive dilemma?
This rule states: “If we have both p and q, then we have r” is logically equivalent to “If we have p, then if we have q, then we have r.”
What is exportation?