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The question has a main statement followed by four statements labelled A, B, C and D. Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.

If I talk to my professors, then I do not need to take a pill for headache.

  1. I talked to my professors.
  2. I did not need to take a pill for headache.
  3. I needed to take a pill for headache.
  4. I did not talk to my professors.
    1. AB only
    2. DC only
    3. CD only
    4. AB and CD
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Best answer
P = I talk to my professors
Q = I do not need to take a pill for headache.
Therefore, both AB(P ⇒ Q) and CD(neg Q ⇒ neg P) are logically consistent, not BA and DC.

Hence Option$:(4) \; \text{AB and CD}$ is the correct answer choice.
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