so you are given a circuit like this and you're asked to determine F or the Boolean expression corresponding to F and then you're asked to draw a simpler circuit if possible which is can you simplify the Boolean expression to come up with a simpler circuit so let us try first getting the expression for f so you have a prime and a so a and a prime will be a zero so here you have B inverted so that's B Prime so the inputs to the orgate are B Prime and B Prime so B prime or B Prime is B Prime this is B Prime here here it just propagates here so B prime or zero will be B Prime and then you have B Prime again so finally f is equals to B Prime so you can write the simplified circuit as b f so instead of using one 2 3 4 5 six Gates you can represent the same circuit using just one gate