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Mark the following true or false. Justify your answers. If the statement is false provide a...

Mark the following true or false. Justify your answers. If the statement is false provide a counter example.

(a) Every simple extension is algebraic.

(b) All simple algebraic extensions of a given subfield of C are isomorphic.

(c) All simple transcendental extensions of subfields of a given subfield of C are isomorphic.

(d) Every minimal polynomial is monic.

(e) Monic polynomials are always irreducible.

(f) Every polynomial is a constant multiple of an irreducible polynomial.

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