Section 1.5 + 1.6

What is a Nested Quantifier?

One which there is a quantifier within the scope of another quantifier

Inside the scopes, communicative, additive inverse, and associative laws apply

What is a proof?

A valid argument that establishes the truth of a mathematical statement

What is an argument?

A sequence of propositions called premises and end with a conclusion

What is a valid argument?

An argument whose conclusion must follow from the truth of the premises of the argument

What is Modus Pones?

(p→q) ^ p therefore q

What is Modus Tollens?

(not q and (p→q)) therefore not p

What is Hypothetical Syllogism?

((p→q) ^ (q→r)) therefore p→r

What is Disjunctive Syllogism?

((p or q) ^ not p) therefore q

What is Addition?

p therefore p or q

What is Simplification?

(p ^ q) therefore p

What is resolution?

(p or q) ^ (not p or r) therefore q or r

What is a fallacy?

Some propositions look like rules of inference but are not tautologies

What is universal instantiation?

Can conclude P(c) is true given ∀xP(x) where c is in the domain

Example: “all my students work hard” “Kate works hard”

What is universal generalization?

Can conclude ∀xP(x) is true given that P(c) is true for all c in the domain

Example: “if i can name any of the 50 states, then I can all 50 states”

What is existential instantiation?

Can conclude that there is a c in the domain such that P(c) is true, given that ƎxP(x) is true

What is existential generalization?

Can conclude ƎxP(x) is true, given that we know there is a c that makes P(c) true

What is conjunction?

((p) ^ (q)) therefore p ^ q