- 1.
P2 is a set including all polynomials of degree less than 2. Let A ⊆ P2 be the vector space spanned by polynomials x2 + 2x + 1, x + 2, x2 − x − 1 and let B ⊆ P2 be the vector space spanned by 1, x, x2. Describe the difference set A − B ≡ {f(x) : f(x) ∈ A, f(x) ∉ B}.
Note: The space spanned by polynomials includes all polynomials that can be written as a linear combination of those polynomials.
- 題型：問答題
- 難易度：尚未記錄
- 2.
Let f1(x) = x2 + 2x + 1. Consider the "multiplication" defined by the logical AND, and "addition" defined by the logical OR. That is, we define
x2 ≡ x ⋅ x ≡ x ∧ x (x AND x), 2x ≡ x + x ≡ x ∨ x (x OR x), and x + c ≡ x ∨ c.
Evaluate f1(FALSE = 0) and f1(TRUE = 1).
- 題型：問答題
- 難易度：尚未記錄
- 3.
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD? Explain why the answer you have
- 題型：問答題
- 難易度：尚未記錄
- 4.
Determine whether the function f(x) = (x + 1)/(x + 2) is a bijection from R to R. Explain why the answer you have.
- 題型：問答題
- 難易度：尚未記錄
Suppose that the function f satisfies the recurrence relation
whenever n is a perfect square greater than 1 and f(2) = 1.
- 5.
Find f(16).
- 題型：問答題
- 難易度：尚未記錄
Suppose that the function f satisfies the recurrence relation
whenever n is a perfect square greater than 1 and f(2) = 1.
- 6.
Find a big-O estimate for f(n).
- 題型：問答題
- 難易度：尚未記錄
- 7.
Find the state table for the nondeterministic finite-state automaton with the state diagram as shown in Figure 1.
- 題型：問答題
- 難易度：尚未記錄
- 8.
Find a deterministic finite-state automaton that recognizes the same language as the nondeterministic finite-state automaton in (a).
- 題型：問答題
- 難易度：尚未記錄