GATE CSE 1998 | Question: 1.5

Question

What is the converse of the following assertion?

• I stay only if you go

• A. I stay if you go
• B. If I stay then you go
• C. If you do not go then I do not stay
• D. If I do not stay then you go

Comments

There are multiple ways to convey your message.

in an implication result is $F$ only in case of $T \implies F$ and true in all other cases.
So one can either convey information about the truth values or false values.

The single $F$ value conveys as much information as three $T$ values.

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If you're confused about the phrase "only if," consider the example below. It will clarify the concept for you :

A: Prime
B: Integer

• A → B (Prime → Integer) is true, because all primes are integers. So, "Prime only if Integer" is correct for "Prime → Integer."

• B → A (Integer → Prime) is false because not all integers are prime (e.g., 4, 6, 8 are integers but not primes).

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A only if B ≡ (A→B)

Answer 1

"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).

Comments

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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learnt something from this question

Answer 2

"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

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From Kenneth H Rosen

 

Answer 3

 

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Answer 4

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

Answer 5

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 

Answer 6

The question test your conceptuals of implication

 

I stay only if you go means

You go is necessary for I stay

Means if you don't go then I can't stay

Means I can stay if you go

 

Now converse of this is

If you go then I stay

 

 

But none of the options are matching, but wait...

Let's say p = I stay and q = you go

Than, option A is I stay if you go, means p if q

And p if q is equal to q→p

 

And we got the statement if you go then i stay

Which is also q → p

 

Therefore option A is correct.