Question

Complete the proof. [}proof{]; 1.A>B, premise; 2. Av~B, premise]:A=B Answer: Dproof(;

Answer 1

Given,

The premises are :

• A > B
• A v ~B

The conclusion to be proved is :

A = B which means A should be equivalent to B that is A ≡ B.

The argument can be proved using the following table :

Statement no.	Statement	Justification
1	A > B	given
2	A v ~B	given
3	~B v A	Commutative property of disjunction on statement 2
4	B > A	Material implication rule on statement 3
5	(A > B) ∧ ( B > A )	Conjunction rule of inference on statements 1 and 4
6	A = B	Definition of equivalence operation on statement 5

The conclusion, A = B, can be derived using the given premises.

Hence, the given argument is proved to be valid.