Answer to Question #239650 in Discrete Mathematics for enKay

Question

In the following argument, determine the validity or otherwise of the statement:
"If the BIOS test runs fine, the CPU and motherboard must be OK. If the CPU and the motherboard and memory are all OK, then there must be a flaw in the OS. The BIOS test runs fine and the memory is OK. Therefore there must be a flaw in the OS."

(I) Write the four(4) propositional statement(s) in the above argument.

(II) State the premise(s) and conclusion in the above argument.

(III) Using a truth table, determine the validity or otherwise of this statement.

Answer 1

(i)

B= BIOS test runs fine

C= CPU and motherboard is OK

M= memory is OK

O = There is a flaw in the OS

(ii)

Premises = $B \to C$

$C \varLambda m \to 0$

$B \varLambda m$

Conclusion =0

(iii)

In bowl All the premise is true, the conclusion is also true. So the argument is valid