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Quiz (Axiomatic Method)

    All of the following poofs should be done in the column format.

(1) Assume the following:

    Definition: is said to be b iff
    Axiom 1:     
    Theorem 1: If is then     
    Theorem 2:

Prove the following theorem:  Theorem: If is then is
    
(2) Assume the following:

    Theorem 1:      
    Theorem 2: If then either or
    
Prove the following theorem. Theorem:
    
(3) Suppose implies either or and assume the following theorems

    Theorem 1:     
    Theorem 2:         
    Theorem 3:
    Theorem 4:
    
Prove the following theorem. Theorem:
    
(4)  Assume the following:

    Axiom 1:
    Axiom 2:
    Theorem 1:
    Theorem 2:
    Theorem 3:         
    
Prove the following theorem. Theorem:      

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