Answer to Question #310311 in Discrete Mathematics for Ali

Question #310311

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) :

1
Expert's answer
2022-03-16T13:12:32-0400

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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