# assignment 代写 | logic代写 | math代写 – Natural Deduction for Propositional Logic

### Natural Deduction for Propositional Logic

assignment 代写 | logic代写 | math代写 – 这个项目是assignment代写的代写题目，涉及logic

Logic & Computation 2018/

### Natural Deduction for Propositional Logic

This assignment is the first of two for Part I of the module, and is worth 5% of the module mark.

It is about arguments in propositional logic, and checking their validity.

When writing natural deduction proofs, you should only use the 8 inference rules that you have been using in earlier exercises (shown overleaf). You are also free to use sequent introduction as long as you give a separate proof of whatever theorem/sequent you want to use.

Present your proofs in the style shown in the module, i.e., where lines of the proof are annotated with the inference rules used and their dependencies, and sub-proofs are clearly marked.

1. Prove, using natural deduction, the validity of the argument: R,QS,(QR)R : S [7 marks]
2. Prove, using natural deduction, the validity of the argument: : (PQ)(PQ) [7 marks]
3. Either prove (using natural deduction) or disprove (by giving a counterexample) the validity of each of the following arguments: (a) : (PQ)(QP) (b) : (PQ)(QP) [11 marks]

Dave Parker 1/2 Assignment I.1, 2018/

Logic & Computation 2018/

### Inference Rules

``````Conjunction () Disjunction ()
A B
AB
``````
``````-introduction
``````

#### A

``````-elimination AB
B
``````
``````-elimination
``````

#### AB

``````-introduction A
BA
``````
``````-introduction
``````

#### C

``````-elimination
``````
``````Implication () Negation ()
A`B
AB
``````
``````-introduction
``````

#### B

``````-elimination
``````

#### A

``````-introduction
``````

#### A

``````-elimination
``````

Dave Parker 2/2 Assignment I.1, 2018/