Answer to Question #147334 in Discrete Mathematics for Hammad

Question

) 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.
iiii. There is a mistake in variable name.

Answer 1

Let

p = a variable is not declared

q = there is a syntax error in the fifth line

r = there is a missing semicolon

s = there is a mistake in variable name

Then we can translate given sentences as:

(1) $p \lor q$

(2) $q \to (r\lor s)$

(3) $\neg r$

(4) $s$

By disjunction introduction ii can be written as:

$q \to r$ (5)

Combining (3) and (5) we have

$q \to r$

$\neg r$

_______

$\neg q$ (by modus tollens) (6)

Combining (1) and (6) we have

$p \lor q$

$\neg q$

________

$p$ (by disjunctive syllogism) (7)

By combining (7) and (4) we have:

($p\land s$ ) — a variable is not declared AND there is a mistake in variable name