Question

In: Computer Science

It is known that the sentence E: if (if P then not (Q or R) else...

It is known that the sentence E: if (if P then not (Q or R) else not P) then (not (Q and S) if and only if (not Q or not S)). Investigate whether I = {S ← false, R ← false, Q '← true, P ← false} interpretations are interpretations for sentence E.

Solutions

Expert Solution

if (if P then not (Q or R) else not P) then (not (Q and S) if and only if (not Q or not S))

The sentence can be written as:

(P→(​​​​​(QR)P))→((QS)→(QS))

Given, the statement

I = {S ← false, R ← false, Q '← true, P ← false}

P Q R S P Q R S (QR) ((QR)P) P→((QR)P) (QS) (QS) (QS)→(QS) (P→((QR)P))→((QS)→(QS))
T T T T F F F F T T T T T T T

As the conclusion is true for the given interpretation.

Therefore, the interpretation I are interpretations for sentence E.


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