igor92
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i) Prove that if a and b are rational numbers, then a + b is a rational number.
ii) Give a counter-example to disprove the statement that if a + b is a rational number, then a + b are both rational numbers.
iii) Use the method of proof by contradiction to prove that if a is a rational number and b is an irrational number, then a + b is an irrational number.

OR maybe anyone here has access to the MEI maths website?
I desperately need answers to this question.

Question 2 from an additional exercise (Proof, section 1: methods of proof)

thank you!
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Small123
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(Original post by igor92)
i) Prove that if a and b are rational numbers, then a + b is a rational number.
ii) Give a counter-example to disprove the statement that if a + b is a rational number, then a + b are both rational numbers.
iii) Use the method of proof by contradiction to prove that if a is a rational number and b is an irrational number, then a + b is an irrational number.

OR maybe anyone here has access to the MEI maths website?
I desperately need answers to this question.

Question 2 from an additional exercise (Proof, section 1: methods of proof)

thank you!
(i) If a and b are rational, what can you say about them?
(ii) Can't really give a hint; just think about it.
(iii) Assume a+b is rational (what does that mean) and then highlight the inconsistency in that rationality to safely assume a+b is irrational through contradiction.
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hamzab
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Dude Its The Holidays! Just Relax!!!
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igor92
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Yes I know but I'm doing my induction. Lucky me

Thank you Small123
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hamzab
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(Original post by igor92)
Yes I know but I'm doing my induction. Lucky me

Thank you Small123
Induction? What?
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Small123
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(Original post by igor92)
Yes I know but I'm doing my induction. Lucky me

Thank you Small123
Not a problem, just so you know the QUOTE button is there to show me if you've replied so it's easier to see a reply . Need any more hints or help just post a new thread or pop back on this one.
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boromir9111
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 x = cos2\theta......... y = sin\theta cos\theta

show that  x^{2} + 4y^{2} = 1

 sin\theta cos\theta = 1/2(sin2\theta)-----> (2y)^{2} = (sin2\theta)^{2}

 4y^{2} = (sin2\theta)^{2}

 x^{2} = (cos2\theta)^{2}

 cos^{2} 2\theta + sin^{2} 2\theta = 1

hence,  x^{2} + 4y^{2} = 1 ......sorry for the rant, just needed to let that out, DAMN
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Small123
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(Original post by boromir9111)
 x = cos2\theta......... y = sin\theta cos\theta

show that  x^{2} + 4y^{2} = 1

 sin\theta cos\theta = 1/2(sin2\theta)-----> (2y)^{2} = (sin2\theta)^{2}

 4y^{2} = (sin2\theta)^{2}

 x^{2} = (cos2\theta)^{2}

 cos^{2} 2\theta + sin^{2} 2\theta = 1

hence,  x^{2} + 4y^{2} = 1 ......sorry for the rant, just needed to let that out, DAMN
:lolwut:
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boromir9111
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(Original post by Small123)
:lolwut:
:mad: :o: :p: :yep: :woo: :rolleyes: :cool: :eek:
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Farhan.Hanif93
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(Original post by boromir9111)
 x = cos2\theta......... y = sin\theta cos\theta

show that  x^{2} + 4y^{2} = 1

 sin\theta cos\theta = 1/2(sin2\theta)-----> (2y)^{2} = (sin2\theta)^{2}

 4y^{2} = (sin2\theta)^{2}

 x^{2} = (cos2\theta)^{2}

 cos^{2} 2\theta + sin^{2} 2\theta = 1

hence,  x^{2} + 4y^{2} = 1 ......sorry for the rant, just needed to let that out, DAMN
That really looked like it was building up inside your head :p:. A bit random however. :lolwut:
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boromir9111
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(Original post by Farhan.Hanif93)
That really looked like it was building up inside your head :p:. A bit random however. :lolwut:
You ain't heard bro, July is the random month....random stuff happens, you should know that being a casanova.....random is up your alley jokes :p:

edit - i know, let's not steal the thread, i'll stop lol.....
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Farhan.Hanif93
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(Original post by boromir9111)
You ain't heard bro, July is the random month....random stuff happens, you should know that being a casanova.....random is up your alley jokes :p:
aha, Casanova. It may appear random but I know my stuff, trust me :p:
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boromir9111
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(Original post by Farhan.Hanif93)
aha, Casanova. It may appear random but I know my stuff, trust me :p:
LMAO.....that's a one to remember, now i call that random comment :p: good one :yep:
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Jonogodden
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rational means 'can be written as a fraction' use that and work from there..

for example A + B

where A = m/n
and B = p/q
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boromir9111
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(Original post by Jonogodden)
rational means 'can be written as a fraction' use that and work from there..

for example A + B

where A = m/n
and B = p/q
Yes :yep:

edit - sorry, thought you was OP, didn't read his username lol, my bad....
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davros
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(Original post by mariellas0005)
thanks ur rlly unhelpful. can u just give some working pls instead of j saying i cant give a hint
Did you mean to comment on a 9-year-old thread??
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mariellas0005
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(Original post by davros)
Did you mean to comment on a 9-year-old thread??
um yes because i was doing the same question. why are u commenting then lol
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zetamcfc
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(Original post by mariellas0005)
um yes because i was doing the same question. why are u commenting then lol
Seen as we aren't here to do the work for you, why would we offer more than hints? Seen as if you just copy what we tell you, you will learn nothing...
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davros
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(Original post by mariellas0005)
um yes because i was doing the same question. why are u commenting then lol
Because it came up as a newly updated thread, and because it wasn't clear from your post who you were actually replying to - unless there was another post which got deleted!!

Tbh it's best to start a new thread of your own if there's a problem you're currently stuck on, rather than bumping a 9 year old thread
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mariellas0005
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(Original post by zetamcfc)
Seen as we aren't here to do the work for you, why would we offer more than hints? Seen as if you just copy what we tell you, you will learn nothing...
the hint didn't help and if you explained it step by step, as a teacher would, maybe I could do it on my own next time.
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