Text - Graeme Forbes, Modern Logic (Oxford: Oxford University Press, 1994) Ch4 (

Question

Text - Graeme Forbes, Modern Logic (Oxford: Oxford University Press, 1994) Ch4 (symbols in text)

Rules of Inference

In giving a proof we have to use rules of inference. These rules are the ones that license or allow or permit us to derive a conclusion from other premises.

1. Use the Rule of Assumptions, &-Elimination (&E), &-Introduction (&I), - Elimination ( E), -Introduction ( I), ~-Elimination (~E), ~-Introduction (~I), and double negation (DN).

Format (EX)

A & B, C & D, (A & D) H H

Solve Below

Use any of the inference rules to prove the following two syntactic sequents:

1. (B & B) G (B & G)

2, B (B & B)

Explanation / Answer

1. (B & B) G

B G by Elimination

(B & G) by Introduction

2, B (B & B) Introduction

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