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"If my computations are correct and I pay the electric bill, then I will run out of money. If I don't pay the electric bill, the power will be turned off. Therefore, If I don't run out of money and the power is still on then my computations are incorrect."

Convert this argument into logical notations using the variables $c, b, r, p$ for propositions of computations, electric bills, out of money and the power respectively. (Where $\neg$ means NOT).

  1. $\text{if } (c \wedge b) \rightarrow r \text{ and } \neg b \rightarrow \neg p, \text{ then } (\neg r \wedge p) \rightarrow \neg c$
  2. $\text{if } (c \vee b) \rightarrow r \text{and } \neg b \rightarrow \neg p, \text{ then } (r \wedge p) \rightarrow c$
  3. $\text{if } (c \wedge b) \rightarrow r \text{ and } \neg p \rightarrow \neg b, \text{ then } (\neg r \vee p) \rightarrow \neg c$
  4. $\text{if } (c \vee b) \rightarrow r \text{ and } \neg b \rightarrow \neg p, \text{ then } (\neg r \wedge p) \rightarrow \neg c$
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(a)if (c∧b)→r and ¬b→¬p, then (¬r∧p)→¬c

"If my computations are correct and I pay the electric bill, then I will run out of money. If I don't pay the electric bill, the power will be turned off. Therefore, If I don't run out of money and the power is still on then my computations are incorrect."

(b)if (c∨b)→r and ¬b→¬p, then (r∧p)→c

"If my computations are correct or I pay the electric bill, then I will run out of money. If I don't pay the electric bill, the power will be turned off. Therefore, If I run out of money and the power is still on then my computations are correct."

(c)if (c∧b)→r and ¬p→¬b, then (¬r∨p)→¬c

"If my computations are correct and I pay the electric bill, then I will run out of money. If  the power turned off then i will not pay the electric bill. Therefore, If I don't run out of money or the power is still on then my computations are incorrect."

 
(d)if (c∨b)→r and ¬b→¬p, then (¬r∧p)→¬c
 
"If my computations are correct or I pay the electric bill, then I will run out of money. If I don't pay the electric bill, the power will be turned off. Therefore, If I don't run out of money and the power is still on then my computations are incorrect."
 
 
Hence,Option(A)if (c∧b)→r and ¬b→¬p, then (¬r∧p)→¬c.
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