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I am new to boolean algebra. I am facing difficulty solving this problem:

Given $f(x) = x \lor a$, for some $f(x)$ and $a$, deduce the value of $x$.

Can someone provide me the solution with example?

Similarly, if $p(x) = x \land a$ for some $p(x)$ and $a$, how can I deduce $x$?

Many thanks in advance.

daOnlyBG
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Deepak
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  • Think about sets: if $Y=X\cap A$ or $Y=X \cup A$, then there are many solutions for $X$ given $A$ and $Y$ – Blah Jan 09 '15 at 06:33
  • Can you tell me the number of probable solution ? Assume x is n bit in length. – Deepak Jan 09 '15 at 06:56

1 Answers1

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If $Y=X \cup A$ then obviously $A \subseteq Y$.

For every subset $R \subseteq A$ the disjoint union $X:=R \cup (Y\setminus A)$ is a solution of $Y=X \cup A$, so there are $2^{\#A}$ solutions

Blah
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