document.write( "Question 1132243: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.\r
\n" ); document.write( "\n" ); document.write( "1. R v ~S
\n" ); document.write( "2. ~R v T
\n" ); document.write( "3. T ⊃ (S • U) \r
\n" ); document.write( "\n" ); document.write( "Conclusion: S ≡ T \n" ); document.write( "

Algebra.Com's Answer #749228 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Here is one way to do a proof derivation to get the conclusion
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

Number	Statement	Lines Used	Reason
1	R v ~S
2	~R v T
3	T --> (S & U)
:.	S = T
4	~S v R	1	Commutation
5	~~S --> R	4	Material Implication
6	S --> R	5	Double Negation
7	~~R --> T	2	Material Implication
8	R --> T	7	Double Negation
9	S --> T	6,8	Hypothetical Syllogism
10	~T v (S & U)	3	Material Implication
11	(~T v S) & (~T v U)	10	Distribution
12	~T v S	11	Simplification
13	~~T --> S	12	Material Implication
14	T --> S	13	Double Negation
15	(S --> T) & (T --> S)	9,14	Conjunction
16	S = T	15	Material Equivalence

\n" ); document.write( "

\n" );