Maths questionn

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

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

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.

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?

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.

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