- 1.
Prove or disprove the following: if H is a nonempty subset of a group G, then H is a subgroup of G if and only if (i) for all a, b ∈ H, then ab ∈ H and (ii) for all a ∈ H, then a−1 ∈ H.
- 題型：問答題
- 難易度：尚未記錄
- 2.
How many n-digit decimal sequences (using digits 0, 1, 2, …, 9) are there in which digits 2, 7, 9, all appear?
- 題型：問答題
- 難易度：尚未記錄
- 3.
Prove or disprove that it is possible to make up exactly any postage of 14 cents or more, using stamps of 3 cents and 8 cents denominations?
- 題型：問答題
- 難易度：尚未記錄
- 4.
Prove or disprove that the language L = {w ∈ {0, 1}* | w has both 01 and 10 as substrings} is regular.
- 題型：問答題
- 難易度：尚未記錄
- 5.
Prove or disprove the following: For any connected planar graph, we have v − e + r = 2, where v, e, and r are the number of vertices, edges, and regions of the graph.
- 題型：問答題
- 難易度：尚未記錄
- 6.
Define the hexadecimal number system, then express 26137 in the hexadecimal system (must show all working).
- 題型：問答題
- 難易度：尚未記錄
- 7.
Determine the constant in (7x2 − (3/x))15 (must show working).
- 題型：問答題
- 難易度：尚未記錄
- 8.
Prove or disprove the following: Zn is a field if and only if n is a prime number.
- 題型：問答題
- 難易度：尚未記錄