Let F be a field. Mark each of the following true or false. 

___ a. Every ideal in F[x] has a finite basis. 

___ b. Every subset of R² is an algebraic variety. 

___ c. The empty subset of R² is an algebraic variety. 

___ d. Every finite subset of R² is an algebraic variety. 

___ e. Every line in R² is an algebraic variety. 

___ f. Every finite collection of lines in R² is an algebraic variety. 

___ g. A greatest common divisor of a finite number of polynomials in R[x] (one indeterminate) can be computed using the division algorithm repeatedly. 

___ h. I have computed Grobner bases before I knew what they were. 

___ i. Any ideal in F[x] has a unique Grabner basis. 

___ j. The ideals (x, y) and (x² , y²) are equal because they both yield the same algebraic variety, namely {(0, 0)}, in R² .