Prove De Morgan$$s Laws for two Boolean variables, $1$ and $2($you can use truth table for this one$).$

$($b$)$ From this, prove the generalized De Morgan$$s Laws for an arbitrarily large number of inputs:

$(123...)=1$

$+2$

$+3$

$++$

$$

$(1+2+3++)=1$

$2$

$3$

$...$

$$

Hint: Use mathematical induction to prove the general case. If you aren$$t familiar with induction,

reach out to me$.$