$14.$ When using the pumping lemma to construct a contradiction, we need to find a good counter$-$example. The counter$-$example should:

a$)$ Satisfy the language $($i$.$e$.,$ a string from the language$)$

b$)$ Include pumping length p such that the length of a string discussed is $>=$ p

For example, L $=\{$w$|$w contains more $0$s than $1$s$\}.$ is $0^$p$1^$p$1$ a counter example? Is $001$ a counter example?

please explain how to do this in simple terms I can learn from for my mid term