Which one of the following is a top-down parser?

Consider the grammar with non-terminals N = { S, C, S₁ }, terminals T = { a, b, i, t, e }, with S as the start symbol, and the following set of rules:

$$\eqalign{ & S \to iCtS{S_1}\,|\,\,a \cr & {S_1} \to eS\,|\,\,\varepsilon \cr & C \to b \cr} $$

The grammar is NOT LL(1) because:

Consider the following two statements:

P: Every regular grammar is LL(1)
Q: Every regular set has a LR(1) grammar

Which of the following is TRUE?

Consider the following two statements:

i. A hash function (these are often used for computing digital signatures) is an injective function.
ii. encryption technique such as DES performs a permutation on the elements of its input alphabet.

Which one of the following options is valid for the above two statements?