Exam 9: Predicate Logic

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize the following, using the scheme of abbreviation provided: Someone tricks everyone but himself. (Px: x is a person; Txy: x tricks y)

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: If everything is round then nothing is square. (Rx: x is round; Sx: x is square)

The relation "being greater than" is

An individual variable is a lowercase letter (v through z) that serves as a placeholder.

When using reductio ad absurdum to prove (x)Fx ⋁ ($x)Gx, we begin by assuming

The identity rule allows us to

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize the following, using the scheme of abbreviation provided: Rachel Carson is the author of Silent Spring. (r: Rachel Carson; s: Silent Spring; Axy: x authored y)

All of the following are well-formed formulas of predicate logic except

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: Brad Pitt is married. (b: Brad Pitt; Mxy: x is married to y)

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: Everybody loves somebody. (Px: x is a person; Lxy: x loves y)

Assuming "z" is not found earlier in the proof, from ($x)($y)((Px • Py) → Lxy) we may validly infer

Which of the following is the best symbolization of "Nothing is unnatural"? (Nx: x is natural.)

One can correctly move from (y)($z)Lzy to ($z)Lzz by UI.

One can correctly move from (x)(y)Fxy → Ga to (y)Fay → Ga by UI.

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: Only artists are happy. (Ax: x is an artist; Hx: x is happy)

In logicese, (x)(Fx • Gx) says

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize the following, using the scheme of abbreviation provided: Erika is the fastest runner. (e: Erika; Rx: x is a runner; Fxy: x is faster than y)

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: Nothing is heavier than itself. (Hxy: x is heavier than y)

The relation "being a friend of" is

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize the following, using the scheme of abbreviation provided: There is exactly one heavyweight champion. (Cx: x is a heavyweight champion)