Week#8

When a question asks us to prove "OR" or "AND" notation, we need to show both end of "OR" and "AND". Intuitively, it's simpler in "AND", and indeed it's simpler. Here are what we have discovered during tutorial. These questions are very useful to note in slog as these can be applied to many other problems.

For all real numbers r,s if r and s are both positive, then .
This can be re-writen as follows:

Now... this statement is false. So we have to prove its negation. Then "AND" notation comes into play. Here is how we have disproved this claim.

It so it's basically proving both side of "AND", because the both sides must be true for A and B to be true.

When it comes to "OR" notation, we need to prove both sides separately. Here is one tutorial example.

 It's in my hand writing, by the way.
The claim seems quite obvious, but it's harder to prove because it's intuitive. When I see this proof, I also convince myself root(r) + root(s) is not equal to root(r+s) indeed.