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- Which implies 1 = T 2 = F 3 = F 4 = F * From this case itself - 2 & 3, 2 & 4, 3 & 4 can be eliminated.
2. No ball is black
- which implies 1 = F 2 = T 3 = F 4 = T *From this 1 & 3 can be eliminated.
3. Some balls are black
- which implies 1 = F 2 = F 3 = T 4 = F * From this 1 & 4 can be eliminated.
So we have FF as a combination for all the four options. Hence none of the options are correct.
How to approach such questions? Create all possible outcomes - and check for all outcomes. Can you think of any other case? Some balls are white? That is covered by some balls are black. As balls can either be white or black only.
@Partho I concur with what @abhinrao24 said. Thats the same logic I used. You've to note that all the 4 given statements can either be True or False. The question, in my opinion, is to find which two co-exist with each other making both true.
@Partho You are not missing anything. You're overdoing it.
The question is- which two of the statement given above can both be true, but cannot both be false?
You need not consider the cases as u have. Just take the 2 statements at a time as standalone units. Read the question carefully, u shud get it.
help me out:
I take statement 2 & 4. Alright?
Case 1: All balls are white = True 2. All balls are white = T 4. No balls are black = T ---- Satisfied.
Case 2: No Balls are black = True 2. All balls are white = T 4. No balls are black = T --- Satisfied!
Case 3: All balls are white = False ( Which means either all balls are black or some balls are black, right? ) 2. All balls are white = F 4. No balls are black = F --- Did not satisfy.
@Partho your answer is correct. None of the options follow.
Option 2 and 4 are the same exact statement, since all balls can either be white or black. Therefore, all balls are white implies that no balls are black. Hence, since they are the same statement they can either both be true or both be false.
The questions asks for statements that can both be true, but cannot both be false. No two such statements are mentioned.
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Comments
Let us analyse all possible outcomes:
1. All balls are black
- Which implies
1 = T
2 = F
3 = F
4 = F
* From this case itself - 2 & 3, 2 & 4, 3 & 4 can be eliminated.
2. No ball is black
- which implies
1 = F
2 = T
3 = F
4 = T
*From this 1 & 3 can be eliminated.
3. Some balls are black
- which implies
1 = F
2 = F
3 = T
4 = F
* From this 1 & 4 can be eliminated.
So we have FF as a combination for all the four options. Hence none of the options are correct.
How to approach such questions? Create all possible outcomes - and check for all outcomes. Can you think of any other case? Some balls are white? That is covered by some balls are black. As balls can either be white or black only.
- Hope my comment helped you.
Opt D seems logical.
You need to take only 2 statements at a time, which are given in the resp options.
In that way, in Partho's 2nd case of no ball is black, v get the reqd case.
Take option 2 & 4.
Is not 2 & 4 both false?
Am I missing something here?
You are not missing anything. You're overdoing it.
The question is- which two of the statement given above can both be true, but cannot both be false?
You need not consider the cases as u have. Just take the 2 statements at a time as standalone units.
Read the question carefully, u shud get it.
I take statement 2 & 4. Alright?
Case 1: All balls are white = True
2. All balls are white = T
4. No balls are black = T
---- Satisfied.
Case 2: No Balls are black = True
2. All balls are white = T
4. No balls are black = T
--- Satisfied!
Case 3: All balls are white = False ( Which means either all balls are black or some balls are black, right? )
2. All balls are white = F
4. No balls are black = F
--- Did not satisfy.
Can you please help!
Option 2 and 4 are the same exact statement, since all balls can either be white or black. Therefore, all balls are white implies that no balls are black. Hence, since they are the same statement they can either both be true or both be false.
The questions asks for statements that can both be true, but cannot both be false. No two such statements are mentioned.
That is what I was trying to explain. You put it in a less technical way.