Problem $1($Pumping Lemma$)$

Use the pumping lemma to show that the following languages are not regular:

$L_1=\{0^n{1}^m$:$n>2m,m0\}.$

$L_2=\{{10}^n{10}^n$:$n0\}.$

$L_3=\{w{w}^R$:win$\{0,1{\}}^{*}\}$ where $w^R$ denotes the reversal of $w.$ For example $(1000{)}^R=0001.$

Recall that the pumping lemma requires you to give a strategy for winning the following game:

The adversary chooses some integer $p.$

You choose a string winL such that $|w|p.$

The adversary chooses strings $x,y,z$ such that $w=xyz$ and $|xy|p,|y|1.$

You choose an integer i and you win if $x{y}^{i}z$ is not in $L.$

Therefore, for each language you ONLY need to answer the following questions $($be concise$)$:

What's your strategy for choosing the string $w$ in the above game?

What's your strategy for choosing the integer $i$ in the above game?

How do you know that $x{y}^{i}z$ is not in $L?$