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# Propositional Logic

If you’re reading this sentence, then propositional logic is meant for you. It's time to demystify the art of formal logic!

The image above has five XOR gates. XOR gates output a 1 if the inputs are a 1 and a 0, otherwise it outputs a 0.

What's the output at the end?

In the image above there are three AND gates and two OR gates. What's the question mark?

If A, B, and C are assigned values of 0 or 1 randomly and independently, what is the probability that the above diagram will be correct?

**HINT:** Of the 8 possible sets of inputs, 4 involve \( C = 1 \) and 4 involve \( C = 0 .\) Treat them separately.

What is C?

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