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1. [9 marks] In this problem we consider a logical system based only on operators @ and
V where V is defined by: p V q =p V ~q.
a. Demonstrate that logical operator ~ can be simulated using only the operators @ and
V. That is, write an expression that uses only these two operators and is logically
equivalent to ~ p. Explain why your answer is correct.
b. Using only @ and V, write an expression which is logically equivalent to p V q. Prove
that the two are logically equivalent using logical equivalences.
c. Finally, use only @ and V to write an expression that is logically equivalent to p / q.
Prove that the two are logically equivalent using logical equivalences.
Since for every truth table over k atomic propositions, we can write a propositional formula
that matches the truth table using ~, V and A, your answers to parts (a), (b) and (c) show
that you can implement any specified logic function using only the @ and V operators.

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