Most Popular Indirect Proof Documents

HW1 Solutions
School: University Of Florida
Course: COT 3100
HW1 Solutions COT 3100 Fall 2014 Section 1.1 8. (8 points) Let p and q be the propositions p: I bought a lottery ticket this week. q: I won the million dollar jackpot on Friday a ¬ p I did not buy a lottery ticket this week. ...

Class Notes 4
School: Carnegie Mellon University
Course: 21 127
... (¬A) ←→ A Proof. This is on the second homework! It's useful to note that the → direction of the proof cannot be done directly, and requires some indirect technique (eg. proof by contradiction or use of law of the excluded middle) 4...

Exam I Study Guide Solutions
School: Johns Hopkins University
Course: AMS 171
... where r ∈ Z. Thus 3(n4 − n2). 6. Let A and B be sets. Prove that A ⊆ B if and only if A∩ ¯ B = ∅. (Do NOT use proof by picture.) ANSWER: Suppose A ⊆ B and let x ∈ A. Then x ∈ B which means x ∈ ¯ B. So A ∩ ¯ B = ∅....

COT3100Fa14_mid1_solutions
School: University Of Florida
Course: COT 3100
... a. If you give a direct proof, what do you assume and what do you prove? b. If you give a proof by contraposition, what do you assume and what do you prove? ... If valid, indicate the rule(s) of inference used in the proof. ...
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HW1 Solutions
School: University Of Florida
Course: COT 3100
HW1 Solutions COT 3100 Fall 2014 Section 1.1 8. (8 points) Let p and q be the propositions p: I bought a lottery ticket this week. q: I won the million dollar jackpot on Friday a ¬ p I did not buy a lottery ticket this week. ...

Homework 9
School: Johns Hopkins University
Course: AMS 171
Discrete Mathematics (550.171) Homework 9 (Due Friday, April 24, 2015) Objectives: The student will explore properties of prime numbers encrypt/decrypt simple messages using the RSA method learn about the fundamentals of graph theory ...

Homework H Solutions on Foundations of Advanced Mathematics
School: North Carolina State University
Course: MATH 225
Math 225 004 Indirect Proofs 1. Write a proof by contraposition to show that for any real number x, if x2 + 2x < 0, then x < 0. Proof. Assume that x is a nonnegative real number. Then 2x is also nonnegative. ...

HW4Solutions
School: University Of Florida
Course: COT 3100
... f(T). Then either b ∈ f(S) or b ∈ f(T). This means either that b = f(a) for some a ∈ S or that b = f(a) for some a ∈ T . In either case, b = f(a) for some a ∈ S ⋃ T , so b ∈ f(S ⋃ T). This shows that f(S) ⋃ f(T) ⊆ f(S + T),...
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Class Notes 4
School: Carnegie Mellon University
Course: 21 127
... (¬A) ←→ A Proof. This is on the second homework! It's useful to note that the → direction of the proof cannot be done directly, and requires some indirect technique (eg. proof by contradiction or use of law of the excluded middle) 4...

Math 123 Finals Mass Tutorial
School: McGill University
Course: BUSINESS 101
... Having the same birthday? ○ Being born in the same month? Practice! #11 A coin is tossed 3 times. Find the probability of ○ Getting at least one head ○ Getting at least two heads ○ Getting an even number of heads Conditional Probab...

Workshop3(sol)
School: University Of British Columbia
Course: MATHEMATIC 220
... The chosen x, y do not satisfy x<y +ϵ for any ϵ > 0. (b) F/T and justify: If x, y ∈ Q, then x + y ∈ Q. Proof. True. ... Solution: The proof is wrong. ...

Workshop2(sol)
School: University Of British Columbia
Course: MATHEMATIC 220
... (a) Statement: ∃x ∈ R such that for any y ∈ R,y ≥ 0, we have xy = 2x. Proof: Let x ∈ R, and y = 2. Then, y ≥ 0, and xy = 2x, as we wanted. ... Proof. ...
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Exam I Study Guide Solutions
School: Johns Hopkins University
Course: AMS 171
... where r ∈ Z. Thus 3(n4 − n2). 6. Let A and B be sets. Prove that A ⊆ B if and only if A∩ ¯ B = ∅. (Do NOT use proof by picture.) ANSWER: Suppose A ⊆ B and let x ∈ A. Then x ∈ B which means x ∈ ¯ B. So A ∩ ¯ B = ∅....

COT3100Fa14_mid1_solutions
School: University Of Florida
Course: COT 3100
... a. If you give a direct proof, what do you assume and what do you prove? b. If you give a proof by contraposition, what do you assume and what do you prove? ... If valid, indicate the rule(s) of inference used in the proof. ...

Final Exam Practice Solutions
School: Johns Hopkins University
Course: AMS 171
... 3. Let x be a composite number. Use direct proof to show that x has a prime factor p such that p ≤ √ x. ... It turns out that G is in fact nonplanar but the proof requires skills you are not re quired to know. ...

Dec 2011 Practice
School: University Of British Columbia
Course: MATH 220
Mathematics 220 Final Examination December 9th 2011 Page 1 of 13 This final exam has 8 questions on 13 ...