We have learned a theoretical result for quadratic probing in Hash table:

Theorem $5\mathrm{.}1.$ New element can always be inserted into a table that is at least half empty and TableSize is prime.

Which of the following interpretations is correct regarding this analysis?

We have learned a theoretical result for quadratic probing in Hash table:

Theorem $5\mathrm{.}1.$ New element can always be inserted into a table that is at least half empty and TableSize is prime.

Which of the following interpretations is correct regarding this analysis?

This analysis indicates that quadratic probing is always very efficient to insert a new element

If the modulo operation is used in the hash function design, then TableSize can be any value, instead of a prime number, to guarantee successful insertion of a new element.

Secondary clustering never happens if the Hash table is at least half empty.

When using quadratic probing, we need to make the load factor smaller than $0\mathrm{.}5,$ i$.$e$.,$

$,$ to reduce the risk of not finding an empty slot.