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.
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