Answer to Question #147068 in Discrete Mathematics for taha

Question

a) We have the following set of information about a computer program, find the mistake in the program using Rules of Inferences.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iv. There is a mistake in variable name.

Answer 1

In this form the premise (iv) implies the conclusion: "There is a mistake in variable name".

I think in the premise (iv) is omitted "not", that is

iv. There is not a mistake in variable name.

Then using the rule of Conjunction Introduction to (iii) and (iv), we conclude that "There is not a missing semicolon and there is not a mistake in variable name".

Next using de Morgan's law $\neg p\land \neg q=\neg(p\lor q)$ we have "It is not true that there is a missing semicolon or there is a mistake in variable name"

Then using to (ii) and "It is not true that there is a missing semicolon or there is a mistake in variable name" the rule of Modus tollens we conclude  "There is not a syntax error in the fifth line".

Finally, using to (i) and "There is not a syntax error in the fifth line" the rule of Disjunctive Syllogism, we conclude that "A variable is not declared".

Therefore, in this case the mistake in the program is the following: "A variable is not declared".