- 1.
- 題型：問答題
- 難易度：尚未記錄
- 2.
What is the probability that an 8-bit byte contains an even number of 1's bits?
- 題型：問答題
- 難易度：尚未記錄
- 3.
In how many ways can we can select a chairman, vice chairman, secretary from 10 persons?
- 題型：問答題
- 難易度：尚未記錄
- 4.
k microprocessors are randomly selected from m microprocessors among which n are defective. What is the probability of obtaining no defective microprocessors?
- 題型：問答題
- 難易度：尚未記錄
- 5.
If a is an integer, the elements of the integers modulo n corresponding to a are denoted by [a]n. In the integers modulo 8, which elements have multiplicative inverses?
- 題型：問答題
- 難易度：尚未記錄
- 6.
Let Sn = 2Sn−1 + n be a recurrence relation satisfying S0 = 0. The solution of Sn is _________.
- 題型：問答題
- 難易度：尚未記錄
Which of the following formula are valid? For each formula that is not valid, must give a counterexample.
- 7.
[∀x (P(x) ⇒ Q(x))] ⇔ [∀x P(x) ⇒ Q(x)]
- 題型：問答題
- 難易度：尚未記錄
Which of the following formula are valid? For each formula that is not valid, must give a counterexample.
- 8.
[∀x P(x) ∨ ∀Q(x)] ⇔ [∀x (P(x) ∨ Q(x))]
- 題型：問答題
- 難易度：尚未記錄
Which of the following formula are valid? For each formula that is not valid, must give a counterexample.
- 9.
[∃x (P(x) ∧ ∀Q(x))] ⇔ [∃x P(x) ∧ ∃x Q(x))]
- 題型：問答題
- 難易度：尚未記錄
- 10.
Define the relation R on Z to be: aRb if a − b is prime. Is R reflexive? symmetric? Transitive? (You must give the reason to support your answer?)
- 題型：問答題
- 難易度：尚未記錄
- 11.
Show that (A ∩ B) × (C ∩ D) = (A × C) ∩ (B × D) where A and B are two sets.
- 題型：問答題
- 難易度：尚未記錄
- 12.
Show that the set of Z × Z is countable, where Z is the set of integer numbers and Z × Z denotes the Cartesian product of Z and Z.
- 題型：問答題
- 難易度：尚未記錄
- 13.
A perfect number is equal to the sum of its divisors. Show that if p and 2p − 1 are
prime, then 2p−1(2p − 1) is perfect.
- 題型：問答題
- 難易度：尚未記錄