Question

The value of $\overline{a}\times (\overline{b}+\overline{c})+\overline{b}\times (\overline{c}+\overline{a})+\overline{c}\times (\overline{a}+\overline{b})=$

• A. $0$
• B. $-1$
• C. $2\overline{a}\times (\overline{b}+\overline{c})$
• D. $\left[\overline{a}\overline{b}\overline{c}\right]$

Answer 1

The correct option is A $0$

$\overline{a}\times (\overline{b}+\overline{c})+\overline{b}\times (\overline{c}+\overline{a})+\overline{c}\times (\overline{a}+\overline{b})$

$=\overline{a}\times \overline{b}+\overline{a}\times \overline{c}+\overline{b}\times \overline{c}+\overline{b}\times \overline{a}+\overline{c}\times \overline{a}+\overline{c}\times \overline{b}$

$=\overline{a}\times \overline{b}+\overline{a}\times \overline{c}+\overline{b}\times \overline{c}-\overline{a}\times \overline{b}-\overline{a}\times \overline{c}-\overline{b}\times \overline{c}$

$=0$(Option A)

Formula:

$\overline{b}\times \overline{a}=-\overline{a}\times \overline{b}$