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): -

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

Symbolizing -All heads of horses are heads of animals, provided that all horses are animals. (Hx = "x is a horse"; Ax = "x is an animal"; Hxy = "x is the head of y".)

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): -

Prove valid -

Symbolizing -Jones will listen to Smith, even though Smith is boring. (j = "Jones"; s = "Smith"; Lxy = "x will listen to y"; Bx = "x is boring".)

Symbolizing -Everyone who loves himself hates someone (or other). (Px = "x is a person"; Lxy = "x loves y"; Hxy = "x hates y".)

Proving invalidity. Show that the following arguments are invalid: -

Symbolizing -All freshmen date only seniors. (Fx = "x is a freshman"; Dxy = "x dates y"; Sx = "x is a senior".)

Symbolizing -If every sinner is sinned against by everyone who is a sinner, then everyone who sins against someone (or other) sins against himself.

Symbolizing -Someone who is a sinner and sins against someone (or other) who is a sinner sins against himself.

Symbolizing -If something is heavy, then anyone who is weak will not lift it. (Px = "x is a person"; Wx = "x is weak".)

Symbolizing -Not all freshmen date every senior.

Prove valid -

Prove valid -

Symbolizing -If anything is heavy, then there is something heavier than this piece of chalk, which happens not to be heavy. (Hx = "x is heavy"; Hxy = "x is heavier than y"; c = "this piece of chalk".)

Proving invalidity. Show that the following arguments are invalid: -

Symbolizing -No freshmen date any seniors.

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