Question

Exercise 2.5.1: Proofs by cases. Prove each statement. Give some explanation of your answer (b) If...

Exercise 2.5.1: Proofs by cases.

Prove each statement. Give some explanation of your answer

(b)

If x and y are real numbers, then max(x, y) + min(x, y) = x + y.

(c)

If integers x and y have the same parity, then x + y is even.

The parity of a number tells whether the number is odd or even. If x and y have the same parity, they are either both even or both odd.

(d)

For any real number x, |x| ≥ 0.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Give a direct proof that the product of two odd integers is odd. 2. Give...
1. Give a direct proof that the product of two odd integers is odd. 2. Give an indirect proof that if 2n 3 + 3n + 4 is odd, then n is odd. 3. Give a proof by contradiction that if 2n 3 + 3n + 4 is odd, then n is odd. Hint: Your proofs for problems 2 and 3 should be different even though your proving the same theorem. 4. Give a counter example to the proposition: Every...
PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE! And...
PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE! And I was thinking of doing 4 cases: 1. x greater than or equal to  0, and y greater than or equal to  0 2. x greater than or equal to 0, y less than 0 3. x less than 0, y greater than or equal to 0 4. x less than 0 , and y is less than 0. Proofs by cases - absolute value. Prove...
1. For each statement that is true, give a proof and for each false statement, give...
1. For each statement that is true, give a proof and for each false statement, give a counterexample     (a) For all natural numbers n, n2 +n + 17 is prime.     (b) p Þ q and ~ p Þ ~ q are NOT logically equivalent.     (c) For every real number x ³ 1, x2£ x3.     (d) No rational number x satisfies x^4+ 1/x -(x+1)^(1/2)=0.     (e) There do not exist irrational numbers x and y such that...
Prove or disprove the following statements. Remember to disprove a statement you have to show that...
Prove or disprove the following statements. Remember to disprove a statement you have to show that the statement is false. Equivalently, you can prove that the negation of the statement is true. Clearly state it, if a statement is True or False. In your proof, you can use ”obvious facts” and simple theorems that we have proved previously in lecture. (a) For all real numbers x and y, “if x and y are irrational, then x+y is irrational”. (b) For...
either prove that it’s true by explicitly using limit laws, or give examples of functions that...
either prove that it’s true by explicitly using limit laws, or give examples of functions that contradict the statement a) If limx→0 [f(x)g(x)] exists as a real number, then both limx→0 f(x) and limx→0 g(x) must exist as real numbers b) If both limx→0 [f(x) − g(x)] and limx→0 f(x) exist as real numbers, then limx→0 g(x) must exist as a real number
DISCRETE MATHS [ BOOLEANS AND LOGIC] Please answer all Exercise 1.7.1: Determining whether a quantified statement...
DISCRETE MATHS [ BOOLEANS AND LOGIC] Please answer all Exercise 1.7.1: Determining whether a quantified statement about the integers is true. infoAbout Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Q(x): x is a perfect square (i.e., x = y2, for some integer y) Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its truth value. (c) ∀x Q(x)...
In class we proved that if (x, y, z) is a primitive Pythagorean triple, then (switching...
In class we proved that if (x, y, z) is a primitive Pythagorean triple, then (switching x and y if necessary) it must be that (x, y, z) = (m2 − n 2 , 2mn, m2 + n 2 ) for some positive integers m and n satisfying m > n, gcd(m, n) = 1, and either m or n is even. In this question you will prove that the converse is true: if m and n are integers satisfying...
You’re the grader. To each “Proof”, assign one of the following grades: • A (correct), if...
You’re the grader. To each “Proof”, assign one of the following grades: • A (correct), if the claim and proof are correct, even if the proof is not the simplest, or the proof you would have given. • C (partially correct), if the claim is correct and the proof is largely a correct claim, but contains one or two incorrect statements or justications. • F (failure), if the claim is incorrect, the main idea of the proof is incorrect, or...
2. Which of the following is a negation for ¡°All dogs are loyal¡±? More than one...
2. Which of the following is a negation for ¡°All dogs are loyal¡±? More than one answer may be correct. a. All dogs are disloyal. b. No dogs are loyal. c. Some dogs are disloyal. d. Some dogs are loyal. e. There is a disloyal animal that is not a dog. f. There is a dog that is disloyal. g. No animals that are not dogs are loyal. h. Some animals that are not dogs are loyal. 3. Write a...
PLEASE READ THE ARTICLES ATTACHED AND ANSWER THE FOLLOWING QUESTION. THE ARTICLES ARE BOTH LISTED PLEASE...
PLEASE READ THE ARTICLES ATTACHED AND ANSWER THE FOLLOWING QUESTION. THE ARTICLES ARE BOTH LISTED PLEASE PROVIDE DETAILED EXPLANATIONS. PLEASE WRITE ONE REFLECTION COMBINING BOTH ARTICLES. The purpose of the Article Reflection is to deepen your engagement with the topic of Epidemiology. It will give you the opportunity to reflect on the current real-life epidemiological issues at hand and help to bring meaning to them. ARTICLE 1: A group of students knew they had covid-19. They hosted a party over...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT