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problem with predicate

I need to solve this predicate , but I don't know how to do that...


¬c xor (¬b∨c) . Please help me if you know?
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roblee
2
There are two ways of doing this.
One is by filling out this truth table, and then checking it against the operators that you've been taught (AND, OR, NAND, XOR, NOR, XNOR etc.) to see which one it's equivalent to:

BC¬b∨c¬c⊕(¬b∨c)00??01??10??11?? \begin{array}{|cc|r|r|} \hline B & C & \neg b \vee c & \neg c \oplus (\neg b \vee c) \\ \hline 0 & 0 & ? & ? \\ 0 & 1 & ? & ? \\ 1 & 0 & ? & ? \\ 1 & 1 & ? & ? \\ \hline \end{array}

The other way is to simplify it algebraically as far as possible, using the following rules in order:

1.

(a xor b) = (a and ¬b) or (b and ¬a)

2.

¬(a or b) = (¬a and ¬b)

3.

(a and (b or c)) = (a and b) or (a and c)

4.

(a or (a and b)) = (a)



Sorry that I can't just give out the answer, I'm sure you understand why.
(edited 12 years ago)

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