To prove the validity of using the method of resolutions:

No Republican or Democrat is not a socialist. Norman Thomas is a socialist. Therefore, he is not a Republican.

I decided the following:

P(x) = "x is a Republican"

Q(x) = "x - d"

S(x) = "x is a socialist"

F1: ∀x∀y∀z ( (P(x) v Q(y)) → !S(z) ) = (CNF) = ( !S(z) v !P(x) ) ^ ( !S(z) v !Q(y) )

F2: S(Norman Thomas)

-----------------------------------

R: !P(Norman Thomas)

Then mn-in clause:

{ !S(z) v !P(x)!S(z) v !Q(y), S(NT) P (NT) }

1) !S(z) v !P(x)

2) !S(z) v !Q(y)

3) S(NT)

4) P (NT)

-----------------

5) !P(NT) (combined 1 and 3)

6) F (connected 5 and 4)

because came to a contradiction, the original assumption was true.

Please tell me if this is the right decision or not (and how, then, should be resolved)

No Republican or Democrat is not a socialist. Norman Thomas is a socialist. Therefore, he is not a Republican.

I decided the following:

P(x) = "x is a Republican"

Q(x) = "x - d"

S(x) = "x is a socialist"

F1: ∀x∀y∀z ( (P(x) v Q(y)) → !S(z) ) = (CNF) = ( !S(z) v !P(x) ) ^ ( !S(z) v !Q(y) )

F2: S(Norman Thomas)

-----------------------------------

R: !P(Norman Thomas)

Then mn-in clause:

{ !S(z) v !P(x)!S(z) v !Q(y), S(NT) P (NT) }

1) !S(z) v !P(x)

2) !S(z) v !Q(y)

3) S(NT)

4) P (NT)

-----------------

5) !P(NT) (combined 1 and 3)

6) F (connected 5 and 4)

because came to a contradiction, the original assumption was true.

Please tell me if this is the right decision or not (and how, then, should be resolved)

asked March 20th 20 at 11:42

0 answer

Find more questions by tags MathematicsDiscrete math