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What is the converse of the following assertion?

  • I stay only if you go
  1. I stay if you go
  2. If I stay then you go
  3. If you do not go then I do not stay
  4. If I do not stay then you go
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5 Answers

Best answer
45 votes
45 votes

"I stay only if you go" is equivalent to "If I stay then you go."

 $\because A \text{ only if } B  \equiv  (A \to B) $

$A=$ "I stay" and $B=$ "You go"

Converse $( A\to B)  =  B\to A$

"If you go then I stay"

Answer is  (A).

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5 votes
5 votes

"If p then q" is same as "$p \rightarrow q"$; which is same as "p only if q".

 

Given: I stay only if you go

This is of the form "p only if q" which means $p \rightarrow q$

Se we can paraphrase it as "If I stay then you go"

 

Clearly, p = I stay.

q = you go.

 

Converse would be $q \rightarrow p$

which is "If you go then I stay"

Option A


From Kenneth H Rosen

 

1 votes
1 votes

I stay only if you go is equivalents to   If I stay then you go.

  A only if B  => A->B

A= "I stay" and B= "You go"
i.e.Conditional: A ---.>B 
     Converse:   B----->A

" If you go then I stay "

Answer is  (A) A if B is equivalence to B -------->A
         "I stay if you go" is also equivalent to "If you go then I stay"

i.e.Conditional: P ---.>Q 
     Converse:  Q----->P 

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