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MEI C3 question Methods of Proof

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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Reply 1
Avatar for Small123
Small123
15
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)(i) If aa and bb are rational, what can you say about them?
(ii)(ii) Can't really give a hint; just think about it.
(iii)(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.
Reply 2
Avatar for hamzab
hamzab
12
Dude Its The Holidays! Just Relax!!!
Reply 3
Avatar for igor92
igor92
OP
2
Yes I know :frown: but I'm doing my induction. Lucky me

Thank you Small123 :smile:
Reply 4
Avatar for hamzab
hamzab
12
igor92
Yes I know :frown: but I'm doing my induction. Lucky me

Thank you Small123 :smile:


Induction? What?
Reply 5
Avatar for Small123
Small123
15
igor92
Yes I know :frown: but I'm doing my induction. Lucky me

Thank you Small123 :smile:

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 :smile:. Need any more hints or help just post a new thread or pop back on this one.
x=cos2θ.........y=sinθcosθ x = cos2\theta......... y = sin\theta cos\theta

show that x2+4y2=1 x^{2} + 4y^{2} = 1

sinθcosθ=1/2(sin2θ)−−−−−>(2y)2=(sin2θ)2 sin\theta cos\theta = 1/2(sin2\theta)-----> (2y)^{2} = (sin2\theta)^{2}

4y2=(sin2θ)2 4y^{2} = (sin2\theta)^{2}

x2=(cos2θ)2 x^{2} = (cos2\theta)^{2}

cos22θ+sin22θ=1 cos^{2} 2\theta + sin^{2} 2\theta = 1

hence, x2+4y2=1 x^{2} + 4y^{2} = 1 ......sorry for the rant, just needed to let that out, DAMN
Reply 7
Avatar for Small123
Small123
15
boromir9111
x=cos2θ.........y=sinθcosθ x = cos2\theta......... y = sin\theta cos\theta

show that x2+4y2=1 x^{2} + 4y^{2} = 1

sinθcosθ=1/2(sin2θ)−−−−−>(2y)2=(sin2θ)2 sin\theta cos\theta = 1/2(sin2\theta)-----> (2y)^{2} = (sin2\theta)^{2}

4y2=(sin2θ)2 4y^{2} = (sin2\theta)^{2}

x2=(cos2θ)2 x^{2} = (cos2\theta)^{2}

cos22θ+sin22θ=1 cos^{2} 2\theta + sin^{2} 2\theta = 1

hence, x2+4y2=1 x^{2} + 4y^{2} = 1 ......sorry for the rant, just needed to let that out, DAMN

:lolwut:
Small123
:lolwut:


:biggrin: :mad: :o: :p: :smile: :frown: :yep: :woo: :rolleyes: :cool: :eek:
boromir9111
x=cos2θ.........y=sinθcosθ x = cos2\theta......... y = sin\theta cos\theta

show that x2+4y2=1 x^{2} + 4y^{2} = 1

sinθcosθ=1/2(sin2θ)−−−−−>(2y)2=(sin2θ)2 sin\theta cos\theta = 1/2(sin2\theta)-----> (2y)^{2} = (sin2\theta)^{2}

4y2=(sin2θ)2 4y^{2} = (sin2\theta)^{2}

x2=(cos2θ)2 x^{2} = (cos2\theta)^{2}

cos22θ+sin22θ=1 cos^{2} 2\theta + sin^{2} 2\theta = 1

hence, x2+4y2=1 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:
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 :wink: jokes :p:

edit - i know, let's not steal the thread, i'll stop lol..... :smile:
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 :wink: jokes :p:

aha, Casanova. It may appear random but I know my stuff, trust me :p:
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 :biggrin: :yep:
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
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....
Reply 15
Avatar for davros
davros
16
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??
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
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...
Reply 18
Avatar for davros
davros
16
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 :smile:
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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