K is algebraically closed and contains a finite field F. L consists of elements of K algebraic over F. S1: L is algebraically closed. S2: L is infinite. Choose truth values.
A polynomial over L has finitely many coefficients algebraic over F. Any root in K is algebraic over the finite extension generated by those coefficients, hence algebraic over F and in L. This proves S1. No finite field is algebraically closed (the polynomial product of x−a over all its elements, minus 1, has no root), so L is infinite. **Both true, C**.
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