True or False and please explain You should use the true not

True or False and please explain. You should use the true (not abused) meaning of Big-O (and Big-Omega), not just the tightest bound.

1. n^2 + n! = Big-Theta(n^n)

2. 100n^2 + n = Big-Theta(n^2)

3. n + sqt.(n) = Big-Theta(n)

4. n * 1/n + log 8 = Big-Theta(1)

5. n + log n^n = Big-Theta(n log n)

1) False since Big Oh of expression n²+n! will give O(n²) if n>1 and n<4 else O(n!)

2) True since the maximum of 100n²+n will be 100n² and as constants can be neglected it will be O(n²)

3) True Since maximum of n and sqrt(n) is n

4) True Since both n*1/n and log8 are constants.

True since maximum of n and nlogn is nlogn