Let p = “The Exams are decided” and q = “The Papers have been set”
Express each of these compound propositions as English sentences. And state
whether it is Contradiction, Tautology or Contingency.
a) ¬ p :
b) p ∨ q :
c) q → p :
d) p ↔ q :
e) ¬ p ∧ q :
f) ¬ p → ¬ q :
g) ¬ q → ¬ p :
h) ¬ q ∨ (¬ p ∧ q) :
Given that
"p =" “The Exams are decided” and "q =" “The Papers have been set”
Solution (a)
"\u00ac p=" ” The exams are not decided”
Solution (b)
"p \u2228 q =" “The exams are decided, or the papers have been set”
Solution (c)
"q \u2192 p =" “If the exams have been decided then the papers have been set”.
Solution (d)
"p \u27f7 q =" “The exams are decided if and only if the papers have been set”
Solution (e)
"\u00ac p \u2227 q =" “The exams are not decided, and the papers have been set”
Solution (f)
"\u00ac p \u2192 \u00ac q =" ” If the exams are not decided, then the papers have not been set”
Solution (g)
"\u00ac q \u2192 \u00ac p =" ” If the paper has not been set then the exams are not decided”
Solution (h)
"\u00ac q \u2228 (\u00ac p \u2227 q)=" "Either the papers have not been set or the papers have been set but the exams are not decided"
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