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Help needed answering a Past Paper question (Groups)


avilezj

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For part a, you can eliminate the p and q on the left hand side by applying the group's binary operation with latex.php?content=p^{-1} and latex.php?content=q^{-1}.

p><p>

By the definition of a group, latex.php?content=p^{-1}p = e, the identity, so they cancel each other out.

p><p>

Do the same thing with q:

p><p>

For part b, look at the second equation. We know that latex.php?content=x^3 = x^2x, so given that latex.php?content=x^3 = x^2x = e, this means that latex.php?content=x^2 = x^{-1}.

So the first equation can be written as

p><p>

Since latex.php?content=x^{-1}x = e they cancel out and we have

p><p>

And just as before, we can get rid of the q from the right hand side to isolate x.

p><p>

If you have any further questions, let me know. I'd be happy to help!

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For part a, you can eliminate the p and q on the left hand side by applying the group's binary operation with latex.php?content=p^{-1} and latex.php?content=q^{-1}.

p><p>

By the definition of a group, latex.php?content=p^{-1}p = e, the identity, so they cancel each other out.

p><p>

Do the same thing with q:

p><p>

For part b, look at the second equation. We know that latex.php?content=x^3 = x^2x, so given that latex.php?content=x^3 = x^2x = e, this means that latex.php?content=x^2 = x^{-1}.

So the first equation can be written as

p><p>

Since latex.php?content=x^{-1}x = e they cancel out and we have

p><p>

And just as before, we can get rid of the q from the right hand side to isolate x.

p><p>

If you have any further questions, let me know. I'd be happy to help!

Thanks, that was really helpful. I didn't know you could just leave it like that.

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Thanks, that was really helpful. I didn't know you could just leave it like that.

No problem :) At least I hope it's okay (since we haven't covered option material yet and this is only based on my own self-study)

Edited by aldld
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