Question

Let a be any element in a boolean algebra B.
If a+x = 1 and ax =0, then

• A. $x=1$
• B. $x=0$
• C. $x=a$
• D. $x=a^{\prime }$

Answer 1

Answer: (D)

$x=a^{\prime }$

Given conditions are $a+x=1$ and $ax=0$.

The value for $a=0$ or $1$.If $a=0$, then $x=1$ to get $a+x=1$

If $a=1$, then $x=0$ to get $ax=0$

So, in both the cases $x=a^{\prime }$

These two conditions will be true, if $x=a^{\prime }$.

Hence, option D is correct.