Let P₁₁(x) be the real vector space of polynomials, in the variable x with real coefficients and having degree at most 11, together with the zero polynomial. Let

E = {s₀(x), s₁(x), ... , s₁₁(x)}, F = {r₀(x), r₁(x), ... , r₁₁(x)}

be subsets of P₁₁(x) having 12 elements each and satisfying

s₀(3) = s₁(3) = ⋯ = s₁₁(3) = 0 , r₀(4) = r₁(4) = ⋯ = r₁₁(4) = 1 .

Then, which one of the following is TRUE?