Question

Consider the set of premises.

$\left\{\right(C\vee E)\to D,(C\wedge B)\leftrightarrow (A\vee \sim D),C\to \sim A,(\sim C\vee \sim B)\to (E\wedge \sim D\left)\right\}$

Which of the following is true?

• A. The premisses are consistent and the conclusion P follows from the premises
• B. The premises are inconsistent and the conclusion P does not follow from the premises
• C. The premise are inconsistent and the conclusion P follows from the premises
• D. The premises are consistent but the conclusion P does not follow from the premises

Answer 1

The correct option is C The premise are inconsistent and the conclusion P follows from the premises

option (c)

Assume that all the premises are true.

Case 1 : C is T (T is for truth value true)

Then A is F. (F is for truth value false)

$SinceC\vee EisT,DisT,$

Therefore $A\vee \sim DisF.$

$Hence,C\wedge BisFand\sim \vee \sim BisT.$

$Thus,E\wedge \sim D$
is T, and D is F, which is impossible.

Case 2 : C is F.

$Thus\sim CisT,$
$andthereforesois\sim C\vee \sim B.$

$ItfollowsthatE\wedge \sim DisT.$

And therefore E is T and D is F.

$SinceC\vee EisT,thenDisT,whichisacontradiction.$
Hence, the given premises are inconsistent.

If the premises are inconsistent then any conclusion P follows from the premises.