Math 381                                                                                                                Name      KEY
Quiz 1

1.  Let $P_{n}$ be a particular statement about the natural number $n$. Suppose that MATH If $P_{2}$ is true, circle all of those below that must be true. 

    MATH
2.  For each $n\in \QTR{Bbb}{N},$ let $P_{n}$ be the following statement:
    MATH

    Show that MATH
    MATH
     

3.  Find all rational solutions of the equation $2x^{4}+3x+1=0.$
    MATH
4.  Let F1 be the following fact (proved in class): If $F$ is a field and $f\in F,$ then $0\cdot f=0.$
     
    Prove the following from the Field Properties and F1 (make sure to justify each step):
    MATH

    MATH

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