Is $( (\lnot p \lor q ) \lor ( p \lor r ) )$ equivalent to $( \lnot p \lor q \lor p \lor r )$? 
Determine whether $( p \land q ) \to ( p \lor ( q \land r ) )$ is tautology or not.

In line 5 of my given picture can I write this
$( (\lnot p \lor q ) \lor ( p \lor r ) )$  as  $( \lnot p \lor q \lor p \lor r )$
If yes then what is this rule called?
My solution:

 A: 
In line 5 of my given picture, can I write this?
$\quad\bigg( (\lnot p \lor q ) \lor ( p \lor r ) \bigg)$  as  $\bigg( \lnot p \lor q \lor p \lor r \bigg)$
If yes then what is this rule called?

It's called the generalised associative law:

If a binary operation is associative, repeated application of the
operation produces the same result regardless of how valid pairs of
parentheses are inserted in the expression. This is called the
generalized associative law.
For instance, a product of four elements
may be written, without changing the order of the factors, in five
possible ways: $${\displaystyle ((ab)c)d}\tag1$$
$${\displaystyle (ab)(cd)}\tag2$$
$${\displaystyle (a(bc))d}\tag3$$
$${\displaystyle a((bc)d)}\tag4$$
$${\displaystyle a(b(cd))}\tag5$$ If the product
operation is associative, the generalized associative law says that
all these formulas will yield the same result. So, unless the formula with omitted parentheses already has a different meaning, the
parentheses can be considered unnecessary and "the" product can be
written unambiguously as $${\displaystyle abcd.}\tag6$$

Here, you've rewritten $(2)$ as $(6),$ which implicitly means $(5).$
