Question

Prove using the notion of without loss of generality that 5x + 5y is an odd...

Prove using the notion of without loss of generality that 5x + 5y is an odd integer when x and y are integers of opposite parity.

Engineering   Computer-Science   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Without loss of genrality Assume that x is odd and y is even.

Let x=2k+1 , where k is some integer

Let y=2i , where i is some integer

5x+5y = 5(2k+1)+5(2i)

            = 10k+5+10i

            = 10k+10i+4+1

            = 2(5k+5i+2)+1

we can label l = 5k+5i+2 and we know l is an integer.

Then from 5x+5y = 2l+1 we know it is an odd integer

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
Without using induction, prove that for x is an odd, positive integer, 3x ≡−1 (mod 4)....
Without using induction, prove that for x is an odd, positive integer, 3x ≡−1 (mod 4). I'm not sure how to approach the problem. I thought to assume that x=2a+1 and then show that 3^x +1 is divisible by 4 and thus congruent to 3x=-1(mod4) but I'm stuck.
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also...
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also odd. 3.b) Let x and y be integers. Prove that if x is even and y is divisible by 3, then the product xy is divisible by 6. 3.c) Let a and b be real numbers. Prove that if 0 < b < a, then (a^2) − ab > 0.
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...
Using PMI prove that the sum of the first n positive odd integers is n2? Is...
Using PMI prove that the sum of the first n positive odd integers is n2? Is there a way to prove it substituting n+1 for n in the LHS and RHS?
Use the Strong Principle of Mathematical Induction to prove that for each integer n ≥28, there...
Use the Strong Principle of Mathematical Induction to prove that for each integer n ≥28, there are nonnegative integers x and y such that n= 5x+ 8y
1)Let ? be an integer. Prove that ?^2 is even if and only if ? is...
1)Let ? be an integer. Prove that ?^2 is even if and only if ? is even. (hint: to prove that ?⇔? is true, you may instead prove ?: ?⇒? and ?: ? ⇒ ? are true.) 2) Determine the truth value for each of the following statements where x and y are integers. State why it is true or false. ∃x ∀y x+y is odd.
Use the method of direct proof to prove the following statements. 26. Every odd integer is...
Use the method of direct proof to prove the following statements. 26. Every odd integer is a difference of two squares. (Example 7 = 4 2 −3 2 , etc.) 20. If a is an integer and a^ 2 | a, then a ∈ { −1,0,1 } 5. Suppose x, y ∈ Z. If x is even, then x y is even.
6) Cramer’s Rule Solve each using Cramer’s rule a) 3x + .5y =10       10x -   ...
6) Cramer’s Rule Solve each using Cramer’s rule a) 3x + .5y =10       10x -    -y = -3 b) x + z +y = 12 -x + 3y - z = 2      -2x + z = -2 7) Proofs Prove the following by induction     1. n3 – n is divisible by 3 for n >=2     2. . Prove that n! < nn forn ≥ 2. Prove directly that: The sum of an integer and its cube...
Without using a calculator, find y' for the function: y = sin-1 (3x)+ln(x)sinh(3x)+ (2x−1)/sqrt(5x+1)
Without using a calculator, find y' for the function: y = sin-1 (3x)+ln(x)sinh(3x)+ (2x−1)/sqrt(5x+1)
Without using the Fundamental Theorem of Arithmetic, use strong induction to prove that for all positive...
Without using the Fundamental Theorem of Arithmetic, use strong induction to prove that for all positive integers n with n ≥ 2, n has a prime factor.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT