Question: Let F be a field with 4 elements {0,1,x,y}. Here 0,1 are the additive and multiplicative neutral element, as usual. a) Prove xy=1. b) Prove
Let F be a field with 4 elements {0,1,x,y}. Here 0,1 are the additive and multiplicative neutral element, as usual.
a) Prove xy=1.
b) Prove xx=y and yy=x.
c) Prove x+y=1.
d) Prove 1+1=0, x+x=0, y+y=0, x+1=y, and y+1=x.
(You can also do parts (a)-(d) in a different order, if you wish.)
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