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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!

XOR Gates

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?

The setup above works like a XOR gate (the output will be 1 if exactly one of the inputs is 1). However, the gate marked by a blue box is missing. What is the gate?

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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