LET P DENOTE THE PROPOSITION “JILL CAN SING,” LET Q DENOTE THE PROPOSITION “DWEEZLE CAN PLAY,”LET R DENOTE THE PROPOSITION “I’LL BUY THE COMPACT DISK,” AND LET S DENOTE THE PROPOSITION “I’LLBUY THE COMPACT DISK PLAYER

23. Let p denote the proposition “Jill can sing,” let q denote the proposition “Dweezle can play,”

let r denote the proposition “I’ll buy the compact disk,” and let s denote the proposition “I’ll

buy the compact disk player.” Then the hypotheses are:

(p ∨ q) → r, p, s.

From p, we may use addition to conclude p ∨ q. From p ∨ q and (p ∨ q) → r, we may use

modus ponens to conclude r. From r and s, we may use conjunction to conclude r ∧ s. Since

r ∧ s represents the proposition “I’ll buy the compact disk and the compact disk player,” we

conclude that the conclusion does follow from the hypotheses.