Question

Joseph lost his notebook. The teacher started questioning students about
the theft.
Catherine said, "Tom did it", Tom said, "Alex did it" while, Martha said, "I
did not do it" and Alex said, "Tom is lying about me".
If only one of the following statements is false, then which of the given
options is correct?​

Answer 1

Statements :-

1. Catherine said, "Tom did it" .
2. Tom said, "Alex did it" .
3. Martha said, "I did not do it" .
4. Alex said, "Tom is lying about me".

If only one of the following statements is true, then which of the given options is correct :-

• Tom stole the pen and Catherine is right .
• Catherine stole the pen .
• Catherine is a liar and Alex is telling the truth .
• Martha did not do it, and is saying the truth .

Answer :-

checking all options we get,

1) Tom stole the pen and Catherine is right .

Conclusion :-

• If tom stole the pen, statement 1 is correct .
• Statement (3) Martha said, "I did not do it" is also correct here.
• Since only 1 statement is true , Option (1) is not possible .

2) Catherine stole the pen .

• if Catherine stole the pen , again martha statement is correct .
• also, alex statement is correct .
• so, option (2) also not possible .

3) Catherine is a liar and Alex is telling the truth .

• if catherine is a liar , tom did not steal the pen .
• if alex is telling the truth , alex did not steal the pen .
• catherine did not steal it . .(See conclusion of Option 2.)
• Then we can conclude that martha stole the pen .

therefore, when martha stole the pen ,

• Statement (1) = wrong .
• Statement(2) = wrong .
• Statement (3) = wrong .
• Statement (4) = correct .

Hence, Option (C) Catherine is a liar and Alex is telling the truth is correct answer.

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Answer 2

Given : Statements :

Catherine said, "Tom did it",

Tom said, "Alex did it"  

Martha said, "I did not do it"

Alex said, "Tom is lying about me".

only one of the statements is FALSE

( Note that here  only one of the statements is FALSE)

There is another Question where only one of the statements is TRUE

 https://brainly.in/question/38267685  Refer this

To Find : who stole pen  ? who is lying

which of the given options is correct ?

Tom stole the pen and Catherine is right

Catherine stole the pen​

Catherine is a liar and Alex is telling the truth

Martha did not do it, and is saying the truth

Solution:

Statements :

Catherine said, "Tom did it",

Tom said, "Alex did it"  

Martha said, "I did not do it"

Alex said, "Tom is lying about me".

only one of the statement is True :

Note that :  Tom said, "Alex did it"    and  Alex said, "Tom is lying about me".

These are contradicting statement and hence one of them is TRUE and another is FALSE

so we get one of the FALSE statement  in these two

Hence Remaining two are TRUE

Catherine said, "Tom did it",   - TRUE=> Tom  stole pen

Martha said, "I did not do it"   - TRUE  => Martha  did  not steal pen

Tom  stole pen =>  Tom said, "Alex did it"   is FALSE

Hence Alex said, "Tom is lying about me".  is TRUE

Final Conclusions :

Tom  stole pen =>  Tom said, "Alex did it"   is FALSE  hence Tom is liar

Tom Stole pen

Catherine , Martha  , Alex are speaking truth

Out of given options :

Tom stole the pen and Catherine is right

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