What is the converse of the following assertion? I stay only if you go.

1998

What is the converse of the following assertion?

I stay only if you go.
  1. A.

    I stay if you go

  2. B.

    If I stay then you go

  3. C.

    If you do not go then I do not stay

  4. D.

    If I do not stay then you go

Attempted by 31 students.

Show answer & explanation

Correct answer: A

Let P mean 'I stay' and Q mean 'you go'. The phrase 'P only if Q' means if P then Q, so the given assertion is: if I stay, then you go. The converse of a conditional statement is formed by swapping the hypothesis and conclusion. Therefore, the converse is: if you go, then I stay, which is equivalently written as 'I stay if you go'. Hence, option A is correct. Option B repeats the original statement. Option C is the contrapositive of the original statement, so it is logically equivalent to the original but it is not the converse. Option D does not match the converse.

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