CODEWITHSUNDEEP
pythonnumpy
cytochrome
cytochrome

Reputation: 549

Determining the values of Boolean variables

Consider two Boolean variables, A and B, and some logical operation(s) on these variables, resulting in C:

C = A [OP] B

where 'OP' could be any combination of '&', '|', '^', '~', etc.

The values of A and B are to be determined.

Is it possible to create a series of tests using logical operations to definitively determine the True/False value of A and B based solely on the value of C for each test?

Since the application is being developed using NumPy, I am most interested in operators found natively in this package.

Upvotes: 1

Views: 59

Answers (1)

loopbackbee
loopbackbee

Reputation: 23332

No, you can't definitely determine A and B if you're simply given the value of C and the operation used.

A single counter-example is needed to disprove it:

C= True
OP= |

There's three possible valid states for A and B: A=True, B=True, A=True, B=False, A=False, B=True

For multiple (user-chosen) tests, we get the same result, if you restrict yourself to &,| and ^ (xor). It's clearly not possible in the general case - since the operations are commutative, you can't tell apart A and B.

As an example, if 

A & B == False
A | B == True
A ^ B == True

both A=True, B=False and A=False, B=True satisfy the conditions.

If we don't apply any restriction at all on the expressions you can test, getting the values of B (for example) is trivial: just evaluate C=(A|~A)|B and the result will be equal to B

But then, if you don't have any restriction, you could just say C=B and test it directly!

Upvotes: 5

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