2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
HW #5(SP2022)
截止时间 2月18日 23:59 得分 95 问题 7
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此测验锁定于 2月18日 23:59。
最新 尝试 1 3,215 分钟 65，满分 95 分
正确答案已隐藏。
此测验的分数: 65，满分 95 分 提交时间 2月18日 22:52 此尝试进行了 3,215 分钟。
We try to prove that if n is an integer, then is divisible by 3.
Which case is the most helpful in a direct proof: assume that
How many cases do we need to discuss in the direct proof?
For each case, we need to show that is
If all of the case holds, the propositional statement is
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
After trying to prove each cases, the result is
n is divisible by 3
答案 3: divisible by 3
neither true or false
none of the above
Prove that .
a. State the assumption and conclusion for direct proof.
b. Construct a direct proof by case analysis.
c. Construct a direct proof without case analysis. Hint: Try to define max and min without using cases.
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Prove that there are no integer solutions to the equation: .
Also, state the assumption and conclusion clearly.
Quick observation: 210 + 210 = 2048 > 2022 and 210 < 2022 < 310 . (Apply Direct Proof Method)
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
didn't prove all cases and didn't show assumption and conclusion
Using proof by contrapositive, prove the following statement:
Suppose m, n∈Z. If both mn and m+n are even, then both m and n are even.
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Not considering all three cases(m_even,n_odd; m_odd, n_odd; m_odd, n_even) -10
Suppose x is a real number. Prove by contrapositive the following statement
If x3+9x7+x ≥ x2+x6+x4, then x≥0
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Consider the statement: there are no integers a and b such that 20a + 4b = 1.
1) What is(are) the assumption(s) if you are to prove this statement using proof by contradiction?
2)What are you trying to show? 3) Construct the proof.
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
For real numbers and , if is rational and is irrational, then is irrational.
1) What is(are) the assumption(s) if you are to prove this statement using proof by contradiction?
2)What are you trying to show? 3) Construct the proof.
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2022/4/28 21:26 HW #5(SP2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
测验分数: 65，满分 95 分
Didn't specify contradiction
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