Maths questionn Watch

Kalabamboo
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I am not too sure what to do here?
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ThomH97
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Do you know what the implies arrows mean with the directions?

Let's say P is 'It is daytime' and Q is 'We can see the Sun'

Then Q ==> P because we can't see the Sun at night. P ==> Q is not true, because it can be daytime but too cloudy to see the Sun. If both directions were true, you can then write P <==>Q.
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Kalabamboo
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(Original post by ThomH97)
Do you know what the implies arrows mean with the directions?

Let's say P is 'It is daytime' and Q is 'We can see the Sun'

Then Q ==> P because we can't see the Sun at night. P ==> Q is not true, because it can be daytime but too cloudy to see the Sun. If both directions were true, you can then write P <==>Q.
Isn't it if and only if?
so for Q ==> P , it means Q is true if and only if P is true

I am struggling with the first question though
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MR1999
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(Original post by Kalabamboo)
Isn't it if and only if?
so for Q ==> P , it means Q is true if and only if P is true

I am struggling with the first question though
But if and only if means it's a two way implication. So for question 1, if x=1, does x²+x-2=0? And if x²+x-2=0, does x=1? Your answer to each question will tell you what you need to know
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Kalabamboo
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(Original post by MR1999)
But if and only if means it's a two way implication. So for question 1, if x=1, does x²+x-2=0? And if x²+x-2=0, does x=1? Your answer to each question will tell you what you need to know
Doesn't it work both ways?
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ThomH97
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(Original post by Kalabamboo)
Isn't it if and only if?
so for Q ==> P , it means Q is true if and only if P is true

I am struggling with the first question though
'If and only if' (or 'iff' for short if your lecturer is cool with that) is <==>. This means that if either is true, then the other must be true as well.

Q ==> P reads as 'Q implies P', so if Q is true, then P must also be true. You can also read Q ==> P as 'if Q is true, then P is true'.

'It is snowing' ==> 'It is cold', for example, but the other way round isn't true.
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Kalabamboo
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(Original post by ThomH97)
'If and only if' (or 'iff' for short if your lecturer is cool with that) is <==>. This means that if either is true, then the other must be true as well.

Q ==> P reads as 'Q implies P', so if Q is true, then P must also be true. You can also read Q ==> P as 'if Q is true, then P is true'.

'It is snowing' ==> 'It is cold', for example, but the other way round isn't true.
Ah ok so for the first question, would it go both ways?
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ThomH97
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(Original post by Kalabamboo)
Ah ok so for the first question, would it go both ways?
Can you start from P and get to Q, with nothing extra?

If x^2 = 9, is it definitely true that x = -3?
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Kalabamboo
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(Original post by ThomH97)
Can you start from P and get to Q, with nothing extra?

If x^2 = 9, is it definitely true that x = -3?
Sure, the example you've given makes sense as x could instead= 3. However I am not really sure how it is related to the question here.
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ThomH97
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(Original post by Kalabamboo)
Sure, the example you've given makes sense as x could instead= 3. However I am not really sure how it is related to the question here.
Indeed, x could be +3 instead. So you can't say that x^2 = 9 implies (means) that x = -3 because it could be +3. But it is true that x = -3 implies x^2 = 9 so we can write x = -3 ==> x = 9.
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Kalabamboo
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(Original post by ThomH97)
Indeed, x could be +3 instead. So you can't say that x^2 = 9 implies (means) that x = -3 because it could be +3. But it is true that x = -3 implies x^2 = 9 so we can write x = -3 ==> x = 9.
Thanks a lot! For part ii) in the ms it says both of them implies each other - I don't quite understand this. Could you please kindly help with this?
Ik it's quite late right now so no worries if not possible
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ThomH97
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(Original post by Kalabamboo)
Thanks a lot! For part ii) in the ms it says both of them implies each other - I don't quite understand this. Could you please kindly help with this?
Ik it's quite late right now so no worries if not possible
Q ==> P is pretty straightforward. For P ==> Q, you're trying to say that if y^3 > 1, then y has to be greater than 1. Can you think of a way for that to be false?

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The only way for it to be false is if you have y less than or equal to 1, yet y^3 > 1, which you can show doesn't happen. This would be a proof by contradiction.
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