Answer to Question #149171 in Discrete Mathematics for buthina

Question

6. Use truth tables to determine whether the argument form is valid. [5 Marks]
a. There is an undeclared variable or there is a syntax error in the first five lines.
b. If there is a syntax error in the first five lines, then there is a missing semicolon
c. There is not a missing semicolon

Answer 1

Premise: There is an undeclared or there is a syntax error in the first five lines

Premise: If there is a syntax error in the first five lines, then there is a missing semicolon

Conclusion: There is not a missing semicolon

Let P=There is an undeclared variable

   Q=There is a syntax error 

    R=There is a missing semicolon

The premises and conclusion can be stated as:

Premise: $P \vee Q$

Premise: $Q \to R$

Conclusion : $\sim R$

We can construct a truth table for $[(P \vee Q) \wedge (Q \to R) ] \to \sim R$

From the table above, we can see that the statement $[(P \vee Q) \wedge (Q \to R) ] \to \sim R$ is not always true. Hence, the argument is INVALID.