Sum of product -

Question

I am having some issue in minimize the following sum of products.

My solution is:

not A and not B or A and ((B and not C)or C)

But I think it is not right.

Answer 1

From the table (the last term is used twice for a simple reduction) $$\begin{aligned}d&=\underbrace{\big(\bar{a} \wedge \bar b \wedge \bar c\big)\vee\big(\bar{a} \wedge \bar b \wedge c\big)}\vee \big(a\wedge b \wedge \bar c\big)\vee \big(a\wedge \bar b \wedge c\big)\vee \big(a\wedge b \wedge c\big)\color{blue}{\vee \big(a\wedge b \wedge c\big)}\\ &=\quad\quad\quad\quad\big(\bar{a} \wedge \bar b )\quad\quad\quad\;\,\vee \underbrace{\big(a\wedge b \wedge \bar c\big)\color{blue}{\vee \big(a\wedge b \wedge c\big)}}\vee \underbrace{\big(a\wedge \bar b \wedge c\big)\vee \big(a\wedge b \wedge c\big)}\\ &=\quad\quad\quad\quad\big(\bar{a} \wedge \bar b )\quad\quad\quad\;\;\vee\quad\quad\quad\quad\big(a \wedge b\big) \quad\quad\quad\;\vee \quad\quad\quad\;\,\big( a \wedge c\big)\end{aligned}$$ so $$\begin{aligned}d&=\big(\bar{a} \wedge \bar b )\vee\big(a \wedge b\big)\vee\big( a \wedge c\big)\\ &=\big(\bar{a} \wedge \bar b )\vee\big(a \wedge(b\vee c)\big)\end{aligned} $$