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Part IV:  Formal Proofs.  Construct a formal proof of validity for statements A through C below using as premisses any of the higher level laws, Professor Userer's laws and the two following items:

(1) Either aggregate investment value increases or the marginal efficiency of capital terminates.
(2) The liquidity preference remains constant and the quantity of money increases.

A.  Aggregate investment value increases or investment opportunities are used up.

B. If liquidity preference remain constant and the quantity of money increases, the either investment opportunities are used up or the marginal efficiency of capital terminates.

C. Either investment opportunities are used up of the marginal efficiency of capital terminates.

Answer A:

1.  V    U	Userer's Sixth Law
2.  T     V	Userer's Fifth Law
3.  V    T	given  /    U     V
4.  (V    U)    (T    V)	1,2 Conj.
5.  U    V	4,3 C.D.

Answer B:

1.  (P    Q)    (R     T)	Higher-Level Law (1)
2.  (R    T)   V	Higher-Level Law (2)
3.  V    (U    T)	Higher-Level Law (4) /   (P    Q)    (U    P)
4,  (P    Q)    V	1,2 H.S.
5. (P    Q)    (U    P)	4,3 H.S..

Answer C:

1.  (P    Q)    (R     T)	Higher-Level Law (1)
2.  (R    T)   V	Higher-Level Law (2)
3.  P      Q	given
4.  [V    (R     T)]    (U      T)	Userer's Second Law /     U    T
5. R      T	1,3 M.P.
6.  V	2,5 M.P.
7.  V    (R      T)	6 Add.
8.  U      T	4,7 M.P.

End of Test on Symbolic Logic

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