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To ensure the safety of autonomous vehicles, the combined complexity of a self-driving car’s decision making process, represented by C0 = log23 + log32 (in this case) is compared to the critical operational threshold H0 = 13/6. Which of the following relations is correct?

Question

To ensure the safety of autonomous vehicles, the combined complexity of a self-driving car’s decision making process, represented by C0 = log23 + log32 (in this case) is compared to the critical operational threshold H0 = 13/6. Which of the following relations is correct?

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Solution

To answer this question, we first need to calculate the value of C0.

C0 = log23 + log32

We know that logab = logcb / logca, so we can convert the base of the logarithms to 10 (as it's the most common base and easier to calculate).

C0 = log102 / log1023 + log103 / log1032

Now, we can use a calculator to find the numerical values:

log102 ≈ 0.30103 log1023 ≈ 1.36173 log103 ≈ 0.47712 log1032 ≈ 1.50515

So,

C0 = 0.30103 / 1.36173 + 0.47712 / 1.50515 C0 ≈ 0.22107 + 0.31707 C0 ≈ 0.53814

Now, let's compare this to H0:

H0 = 13/6 ≈ 2.16667

So, C0 < H0. Therefore, the complexity of the self-driving car’s decision making process is less than the critical operational threshold.

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