Computers and Technology, 05.10.2019 14:30 lllamasarebae3076

"if x and y are odd integers, then x + y is even"

give a proof by contradiction of this theorem.

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Answer from: jos0305

Hello!

The statement is "if x and y are odd integers, then x + y is even"

and we want to prove it by contradiction.

Suppose that we have x and y odd numbers, and suppose that his addition is odd.

We know that an odd number can be writen as (2n +1) (and a even number can be written as 2n) where n is an integer number; then:

x = (2k + 1) and y = (2m + 1)

and x + y = j, where j is also a odd number, then j = (2h + 1)

then:

2k + 1 + 2m + 1 = 2h + 1

2(k + m) + 2 = 2h + 1

2(k + m) +1 = 2h

if k and m are integers, then k + m is also an integer, suppose that k + m = g

then 2g + 1 = 2h

this says that in odd number is equal to an even number, then we have a contradiction, and the addition of two odd numbers cant be an odd number.

Answer from: Quest

My favorite is "be concise."have you ever received an email and had to read a page full of information? by the time you finished reading it, you had to re-read it? i have even hit "reply" so that i could break it down into separate paragraphs and send it back to myself.what is concise? get to the point, fast. when opening an email like this, some will close it or print it to read later.i learned to use the subject line to prepare the reader for content. such as, "need on (blank), " "info only re: (blank)," "request input on (blank)," "read before (blank) meeting." these are just some.if you are asking for something, make that your first sentence. follow this by who, what, when, where, and how. use these, as necessary. example; (1) who (who needs it and or who does it), (2) what (specific description of what is needed), (3) when (specific, i need this by 8: 00 am monday or i need this by 10: 00 am today), (4) where (does it have to be printed and taken to someone, maybe the place of the meeting), (5) how (i need it scanned or faxed back to me at this email address, provide me with a hard copy).do not send yet. re-read it. did some spell check change a word? maybe let someone else read it for understanding. you want to avoid multiple emails asking for clarification. if important, put a read receipt on it. you will know it was opened, not necessarily read.end with a you.

Answer from: Quest

The answer is b.
hope it’s

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"if x and y are odd integers, then x + y is even"

give a proof by contradiction of this...

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