Exam 10: Relational Predicate Logic

Translations. Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage): -

Theorems of logic. Prove that the following are theorems of logic: -

Symbolizing -Some freshmen date no seniors.

Theorems of logic. Prove that the following are theorems of logic: -

Symbolizing -No freshmen date all seniors.

Prove valid -

Symbolizing -If something is heavy, then Art won't lift it. (Hx = "x is heavy"; a = "Art"; Lxy = "x will lift y".)

Translations. Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage): -

Symbolizing -All who have sinned have come short of the glory of God. (Px = "x is a person"; Sx = "x has sinned"; Cxy = "x has come short of y"; g = "the glory of God.")

Translations. Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage): -

Symbolizing -Some freshmen date only seniors.

Symbolizing -Some freshmen date every senior.

Theorems of logic. Prove that the following are theorems of logic: -

Symbolizing -All sinners who sin against someone who is a sinner are sinned against by someone who is a sinner. (Sx = "x is a sinner"; Sxy = "x sins against y".)

Theorems of logic. Prove that the following are theorems of logic: -

Translations. Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage): -

Translations. Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage): -

Symbolizing -Not all freshmen date seniors.