Here are the answers for the first five questions:

1. A collection of events is exhaustive if they, when taken together, constitute the entire sample space.

2. The disjunction of the sentences 'It is now.' and 'It is never.' is: (B) It is now or never.

3. All equivalent sets are equal, but all equal sets are not equivalent. Answer: (D) equivalent, equal

4. What is the value of sin(90⁰ - θ)? (D) Cos(θ) (This is a standard trigonometric identity: sin(90° - θ) = cos(θ))

5. The Constant Function Rule states that 'If f(x) = k, being a constant, then: (C) f'(x) = 0 (The derivative of a constant function is always zero.)

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Would you like more details on any of these questions, or do you have any additional queries?

Follow-up Questions:

1. What are mutually exclusive events in probability theory?
2. Can you explain the difference between conjunction and disjunction in logic?
3. How do equivalent sets differ from equal sets?
4. What are the other key trigonometric identities like sin(90° - θ)?
5. How does the derivative behave for other types of functions?

Tip:

For trigonometric questions, always remember to refer to fundamental identities like $\sin(90^\circ - \theta) = \cos(\theta)$.