Exam 9: Predicate Logic

When using the finite universe method for a two-object universe (containing a and b), the statement ($x) Fx would be translated as

(x)(Hx → Mx) is logically equivalent to (x)(~Hx ⋁ Mx).

($x)(Dx → Cx) is a particular affirmative statement.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: All of Natalie's sailboats are faster than Ron's. (Sx: x is a sailboat; Bxy: x belongs to y; Fxy: x is faster than y; n: Natalie; r: Ron)

The occurrence of the variable "y" in (x)(Fx • Gy) is free.

"There are at least two people in the presidential race" can best be symbolized (Px: x is a person; Rx: x is running for president) as

In logicese, (x)~Fx says

A precisely described and finite procedure for solving a problem is called

Which of the following is a correct inference from (x)Fx → Ga?

One can correctly move from (x)[(~x = b) → Fc] to (x)[(~b = x) → Fc] by the rule of Symmetry.

Gx is a statement.

Which of the following is an instance of (x)[Lx → ($y)(Ly → Gyx)]?

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: The relation "being equal to" is transitive. (Exy: x is equal to y)

Which of the following is an incorrect application of Leibniz's law?

Logical equivalence is a symmetrical relation.