so if
is even then n must be even.
QUESTION 6 1. 2 Give a direct proof that if n' is even, then n is...
(2) x + 1 is even -> x^2 is odd (hint: use a direct proof) (a) (0.5 points) What are you assuming is true: (b) (0.5 points) What are you proving is true: (c) (1 point) Complete the proof:
please help me with this question:
19. Give a story proof that 72 +3 for all integers n 2 2. Hint: Consider the middle number in a subset of (1,2.,n +3) of size 5.
19. Give a story proof that 72 +3 for all integers n 2 2. Hint: Consider the middle number in a subset of (1,2.,n +3) of size 5.
Discrete Mathematics. (a) Use the method of generalizing from the generic particular in a direct proof to show that the sum of any two odd integers is even. See the example on page 165 of the 5th edition of Discrete Mathematics with Applications, Metric Version for how to lay this proof out. (b) Determine whether 0.151515... (repeating forever) is a rational number. Give reasoning. (c) Use proof by contradiction to show that for all integers n, 3n + 2 is...
1 point Prove the following statement: If n2 is even, then n is even. Order each of the following sentences so that they form a logical proof. Proof by Contrapositive: Choose from these sentences: Your Proof: Suppose n is odd. Then by definitionn 2k +1 for some integer k Required to show if n is not even (odd), then n is not even (odd). Thus n2(2k1)2. n24k2 4k1. 22(22+2k) +1 Thus n2 (an integer) +1 and by definition is odd....
please answer questions #7-13
7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
please answer the question using 0 & 1 instead of T &
F
7. (10) Give a direct proof and an indirect proof of the following:
7. (10) Give a direct proof and an indirect proof of the following:
Give a short proof for why every graph has an even number of vertices of odd degree.
Discrete Mathematics Question 1: (a) Use the method of generalizing from the generic particular in a direct proof to show that the sum of any two odd integers is even. See the example on page 152 (4th edition, Discrete Mathematics with Applications) for how to lay this proof out. (b) Determine whether 0.151515... (repeating forever) is a rational number. Give reasoning. (c) Use proof by contradiction to show that for all integers n, 3n + 2 is not divisible by...
Give a proof or counterexample, whichever is appropriate. 1. For any sets A and B, (A ∩ B = ∅) AND (A ∪ B = B) ⇒ A = ∅ 2. An integer n is even if n2 + 1 is odd. 3. The converse of the assertion in exercise 62 is false. 4. For all integers n, the integer n2 + 5n + 7 must be positive. 1.65. For all integers n, the integer n4 + 2n2 − 2n...
UUIDOR Quiz 2 - Ma Consider the following theorem. Theorem: The sum of any even integer and any odd integer is odd. Six of the sentences in the following scrambled list can be used to prove the theorem. By definition of even and odd, there are integers rands such that m = 2r and n = 2s + 1. By substitution and algebra, m + n = 2r + 25 + 1) = 2(r + s) + 1. Suppose m...