in Mathematical Logic edited by
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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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$P\rightarrow Q$  can also be written as 

$\bullet$  if P then Q

$\bullet$  If P, Q

$\bullet$  Q if P

$\bullet$  Q when P

$\bullet$  Q unless ~P

$\bullet$  P only if Q

$\bullet$  P implies Q

$\bullet$  Q whenever P

$\bullet$  Q follows from P

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This is also possible for $P\rightarrow Q$

$P$ is sufficient for $Q$

A necessary condition for $P$ is $Q$

$Q$ is necessary for $P$

A sufficient condition for Q is $P$

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YesπŸ‘
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4 Answers

37 votes
37 votes
Best answer

"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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4 Comments

I stay only if you go  is equivalent to if I stay then you go. check again

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Now I understood the meaning of "only if".... I thought A only if B means B->A.

But, A only if means A->B,

So ans is A.

Thanks for the explanation Anirudh...
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A only if B $\equiv$ A $\rightarrow$ B

Given : A $\rightarrow$ B  . We have to find all which given below for A $\rightarrow$ B ?

Direct = A $\rightarrow$ B

Converse = B $\rightarrow$ A

Inverse =  ~A $\rightarrow$ ~B

COntrapositive = ~B $\rightarrow$ ~A

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4 votes
4 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

 

0 votes
0 votes
option a.  converse is B->A can also be written as "A if B" thats u ans (a)
0 votes
0 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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Answer:

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