A function $f(a,b,c)$ is $0$ when at least two of its inputs are $0,$ otherwise it is $1.$

$4\mathrm{.}1.$ Write down the truth table $(1p)$

$4\mathrm{.}2.$ Provide the products$-$of$-$sum $($POS$)$ equation using a K$-$map $(1$p$)$

$4\mathrm{.}3.$ From the POS equation, determine the SOP equation using Boolean algebraic principles. $(1$p$)$

$4\mathrm{.}4.$ Draw the Venn diagram $(1$p$)$