Part 1: Choose two of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the arguments. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. 1.(G • P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G • ~L) → K 2.(S v T) ↔ ~E, S → (F • ~G), A → W, T → ~W, therefore, (~E • A) → ~G 3.(S v T) v (U v W), therefore, (U v T) v (S v W) 4.~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B 5.~S → (F → L), F → (L → P), therefore, ~S → (F → P) Part 2: Below are basic arguments in English. Choose two arguments and translate those argument into the symbolism of predicate logic. You do not need to do a proof. Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life). Some wars are just. No war of aggression is just. Therefore, there are wars that are not wars of aggression. (Wx = x is a war, Jx = x is just, Ax = x is a war of aggression). At least one instance of intentional killing is not wrong. But every murder is wrong. Hence, some instances of intentional killing are not murder. (Kx = x is an instance of intentional killing, Wx = x is wrong, Mx = x is murder) Only things that have human bodies are human. No soul has a human body. Only souls survive the death of the body. Therefore, no humans survive the death of the body. (Bx = x has a human body, Hx = x is human, Sx = x is a soul, Dx = x survives the death of the body.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Part 1:

Choose two of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the arguments. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8.

1.(G • P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G • ~L) → K

2.(S v T) ↔ ~E, S → (F • ~G), A → W, T → ~W, therefore, (~E • A) → ~G

3.(S v T) v (U v W), therefore, (U v T) v (S v W)

4.~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B

5.~S → (F → L), F → (L → P), therefore, ~S → (F → P)

Part 2:

Below are basic arguments in English. Choose two arguments and translate those argument into the symbolism of predicate logic. You do not need to do a proof.

Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life).
Some wars are just. No war of aggression is just. Therefore, there are wars that are not wars of aggression. (Wx = x is a war, Jx = x is just, Ax = x is a war of aggression).
At least one instance of intentional killing is not wrong. But every murder is wrong. Hence, some instances of intentional killing are not murder. (Kx = x is an instance of intentional killing, Wx = x is wrong, Mx = x is murder)
Only things that have human bodies are human. No soul has a human body. Only souls survive the death of the body. Therefore, no humans survive the death of the body. (Bx = x has a human body, Hx = x is human, Sx = x is a soul, Dx = x survives the death of the body.

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