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.

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

(Q

R)

(

(QR)P)

P→(

(QR)P)

(QS)

(QS)→(QS)

(P→((QR)P))→((QS)→(QS))

T

F

T

As the conclusion is true for the given interpretation.

Therefore, the interpretation I are interpretations for sentence E.

venereology answered 1 year ago

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