October 20, 2023
October 20, 2023
October 20, 2023
GATE 2006
October 20, 2023
 Question 8
“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 ¬ means NOT)
 A if (c Λ b)→r and ¬b→p, then (¬r Λ p)→¬c B if (c ∨ b)→r and ¬b→¬p, then (r Λ p)→c C if (c Λ b)→r and ¬p→b, then (¬r ∨ p)→¬c D if (c ∨ b)→r and ¬b→¬p, then (¬r Λ p)→¬c
Question 8 Explanation:
We can represent ,
“c” for my computations are correct
“b” for I pay the electric bill.
“r” for I will run out of money
“p” for the power is on.
(c Λ b) means my computations are correct and I pay the electric bill.
(¬r Λ p) means I don’t run out of money and the power is still on.
According to the statement , the option -(A) is correct.
Question 8 Explanation:
We can represent ,
“c” for my computations are correct
“b” for I pay the electric bill.
“r” for I will run out of money
“p” for the power is on.
(c Λ b) means my computations are correct and I pay the electric bill.
(¬r Λ p) means I don’t run out of money and the power is still on.
According to the statement , the option -(A) is correct.