Mark each of the following true or false. ____ a. The number is transcendental over Q.

Question:

Mark each of the following true or false.
____ a. The number π is transcendental over Q.
____ b. C is a simple extension of R
____ c. Every element of a field F is algebraic over F.
____ d. R is an extension field of Q.
____ e. Q is an extension field of Z₂.
____ f. Let α ∈ C be algebraic over Q of degree n. If f(α) = 0 for nonzero f(x) ∈ Q[x], then (degree f(x)) ≥ n.
____ g. Let α ∈ C be algebraic over Q of degree n. If f(α) = 0 for nonzero f(x) ∈ R[x], then (degree f(x)) ≥ n.
____ h. Every nonconstant polynomial in F[x] has a zero in some extension field of F.
____ i. Every nonconstant polynomial in F[x] has a zero in every extension field of F.
____ j. If x is an indeterminate, Q[π] ≈ Q[x].