CRE 1 - Basics | LR - Binary Logic

Answer: Option D

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Explanation :

Any of truth-teller, liar or alternator can say “I am a truth-teller”

Hence, option (d).

Answer: Option C

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Explanation :

A truth-teller will never say “I am a liar” because that would be a lie and he cannot speak a lie.

A liar will never say “I am a liar” because that would be true and he cannot speak the truth.

∴ Only an alternator can say “I am a liar”.

Hence, option (c).

Answer: Option A

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Explanation :

A truth-teller will never say “I am an alternator” because that would be a lie and he cannot speak a lie.

A liar can say “I am an alternator” because that would be a lie.

An alternator can say anything.

∴ Varun cannot be a truth-teller.

Hence, option (a).

Answer: Option B

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Explanation :

Assuming,

Case 1: Gautam is truth teller i.e., his both statements should be correct.

But his first statemen says that Umesh is the truth-teller which cannot be the case since they are all of different kinds.

∴ Gautam is not the truth-teller.

Case 2: Bheem is the truth-teller i.e, his both statements should be correct.

⇒ His second statement is true and his first statement indicates that Gautam is the liar and Umesh is the alternator.

Checking for statements of Gautam (liar): His both statements are false, which fits well with our assumption.

Checking for statements of Umesh (alternator): His first statement is false and second is true, which also fits well with our assumption.

∴ Gautam is liar, Bheem is truth-teller and Umesh is alternator.

Case 3: Umesh is the truth-teller i.e, his both statements should be correct.

This cannot be case because Umesh’s second statement is contradictory.

∴ Gautam is liar.

Hence, option (b).

Answer: Option B

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Explanation :

Assuming,

Case 1: Harsh is the truth-teller i.e., both his statements are correct.

∴ Harsh is the mechanic, Akash is liar and Raju is alternator.

Checking for statements of Akash (liar): His both statements are false, which fits well with our assumption.

Checking for statements of Raju (alternator): His both statements are false, which contradicts our assumption.

∴ Harsh cannot be the truth-teller.

Case 2: Akash is the truth-teller i.e., both his statements are correct.

∴ Akash is the mechanic, Raju is liar and Harsh is alternator.

Checking for statements of Raju (liar): His first statement is true which contradicts our assumption.

∴ Akash cannot be the truth-teller.

Case 3: Raju is the truth-teller i.e., both his statements are correct.

∴ Akash is the mechanic, Harsh is liar and Akash is alternator.

Checking for statements of Harsh (liar): His both statement are false, which fits well with our assumption.

Checking for statements of Akash (alternator): His first statement is true and second statement is false, which fits well with our assumption

∴ Akash is the mechanic.

Hence, option (b).

Answer: Option A

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Explanation :

Assuming,

Case 1: Sachin potted the ball ⇒ Saching and Sourav’s statements are correct and Vinod’s statement is false.

Case 2: Sourav potted the ball ⇒ All three statements are false.

Case 3: Vinod potted the ball ⇒ All three statements are true.

Since there has to be at least one true and one false statement, case 1 is applicable here.

Hence, option (a).

Answer: Option A

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Explanation :

Assuming, 

Case 1: BJP wins the election ⇒ Now only C would be wrong.

Case 2: Congress wins the electio ⇒ Now B and C would be wrong.

Case 3: None of them wins the election ⇒ Now A and B would be wrong.

Since only 1 of them is wrong hence, Case 1 is applicable here.

∴ BJP wins the election.

Hence, option (a).

Answer: Option B

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Explanation :

Assuming,

Case 1: Ankush robbed the bank ⇒ only Mahesh is telling the truth.

Case 2: Mahesh robbed the bank ⇒ Ankush and Ganesh are is telling the truth.

Case 3: Ganesh robbed the bank ⇒ Ankush and Mahesh are telling the truth.

Since only one of them is telling the truth Case 1 is applicable here.

∴ Ankush robbed the bank.

Hence, option (b).

Answer: Option D

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Explanation :

Assuming,

Case 1: A is the knight ⇒ B and C can be spy or knave.

This fits wells with statements made by B and C.

Case 2: B is the knight ⇒ A is spy and C is knave.

This fits wells with statements made by A and C.

Case 3: A is the knight ⇒ A is spy and B is knave.

This contradicts statement made by B.

∴ Based on case 1 and 2, any three of them can be the spy.

Hence, option (d).

Answer: Option B

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Explanation :

Eesha lies on Monday, Tuesday and Wednesday whereas Asha lies on Thursday, Friday and Saturday. Other days they will say the truth. We can make the following table :

​​​​​​​Asha can say I was lying yesterday only on Thursday and Sunday.

Esha can say I was lying yesterday only on Thursday and Monday.

∴ Both of them can say yesterday I was lying at the same time only on Thursday.

Hence, option (b).