Exam 13: Identity

Symbolize, using the indicated letters: -One and only one sinner sins against all sinners.

Symbolize, using the indicated letters: -The largest Great Lake is Lake Superior (Gx = "x is a Great Lake"; Lxy = "x is larger than y"; s = "Lake Superior")

Symbolize, using the indicated letters: -Anything that is heavier than itself is heavier than something else.

Proofs with identity. Prove the validity of the following arguments: -

Symbolize, using the indicated letters: -The capitol of Ohio is a river town. (Cxy = "x is a capitol of y"; Rx = "x is a river town"; o = "Ohio")

Proofs with identity. Prove the validity of the following arguments: -

Symbolize, using the indicated letters: -No sinner is sinned against by all other sinners.

General Theory -Explain why translating "s is visible to Jane" as a material conditional, such as "if s is near Jane (and the line of sight is unobstructed, etc.) then it will be seen by her," seems to be inadequate.

Symbolize, using the indicated letters: -The capitol of Ohio is Columbus. (c = "Columbus")

Symbolize, using the indicated letters: -Something that is heavier than everything else is still not heavier than itself. (Hxy = "x is heavier than y ".)

Symbolize, using the indicated letters: -The sinner who sins against every sinner sins against himself.

General Theory -Use an example to explain the distinction that is made between sentences and propositions.

Proofs with identity. Prove the validity of the following arguments: -

Symbolize, using the indicated letters: -If some sinners are not sinned against by others, then for any nonsinners, they aren't sinned against by any sinners.

Symbolize, using the indicated letters: -All sinners who sin against everyone else, sin against themselves.

General Theory -Determine the status of the following relations with respect to symmetry, transitivity, and reflexivity: a) ______________ respects _ _ _ _ _ _ _ _ _ b) ______________ resembles _ _ _ _ _ _ _ _ _ c) ______________ is a child of _ _ _ _ _ _ _ _ _

Symbolize, using the indicated letters: -The capitol of Ohio is not the largest city in Ohio. (Ixy = "x is a city in y")

General Theory -Give two reasons why some think that universal statements cannot be adequately expressed as conjunctions.

Symbolize, using the indicated letters: -At most one sinner sins against everyone else who is a sinner. (Quite difficult)

Symbolize, using the indicated letters: -Every state has exactly two senators. (Sx = "x is a state"; Sxy = "x is a senator from y")