Binary Logic: Solved Examples

Go through the given solved examples based on Binary Logic to understand the concept better.
  1. Three persons A, B and C gave these statements:
    A said, either Freedom Party or Green Party won the elections.
    B said, Freedom Party won.
    C said, neither Freedom Party nor Green Party won the elections.
    Of these persons, only one person is wrong.
    Who won the elections?
    1. Freedom Party
    2. Green Party
    3. Data Inadequate
    4. None of these
    Sol: Option 1
    Solution: As only one person is wrong, so other two persons are telling the truth. Assume that the Freedom Party won the election. So, the statements of A and B are true as they satisfy our condition that 2 of them are truth tellers. Hence the Freedom Party wins the election.
    If you assume that the Green Party won the election, statements of B and C become false which is violating the given condition.
  2. The police rounded up Tolu, Molu and Golu yesterday because one of them was suspected of robbing the local bank. The 3 suspects gave following statements after intensive questioning:
    Tolu: I’m innocent.
    Molu: I’m innocent.
    Golu: Molu is the guilty one.
    Who robbed the bank among the three persons, if only one of the statements will be true?
    1. Molu
    2. Tolu
    3. Golu
    4. None of these
    Sol: Option 2
    Solution: Let us assume Molu as the robber. So we can see that statement of Tolu is correct. But statement given by Molu is wrong. The statement given by Golu is also correct as he is pointing towards Molu as the robber. So 2 statements are correct which is the violation of the given condition.
    Assume Tolu is the robber. Then we can see that except Molu’s statement, remaining two statements becomes false. So Tolu is the robber.
DIRECTIONS for questions3 – 4: Consider the following statements and answer the questions that follow.
Three criminals were arrested for shop lifting. However, when interrogated, only one of them told the truth in both his statements, while the other two each told one true statement and one lie. The statements were:
Ti-Ti: (a) Chi-chi passed the goods.
(b) Ki- Ki created the diversion.
Ki-Ki : (a) Ti-Ti passed the goods.
(b) I created the diversion.
Chi-Chi : (a) I took the goods out of the shop.
(b) Ki-Ki passed goods.
  1. Who created the diversion?
    1. Ti-Ti
    2. Chi-chi
    3. Ki-Ki
    4. Either 1 or 2
    Sol: Option 3
    Solution: Let us assume that Ti – Ti speaks the truth. Then as his both statements are true, so we get the arrangement as Chi -Chi passed the goods, Ki-Ki created diversion and Ti-Ti took goods out of shop.
    But when this arrangement is validated as per the statement, we find that there is one Truth Teller, one Liar and one alternator. This scenario violates the given condition that there is one truth teller and two alternators. So our assumption that Ti – Ti is the truth teller is wrong.
    Assume that Ki-Ki speaks the truth. (F- False, T- True). Then we get the following table:
      1st 2nd
    Ti-Ti F T
    Ki-Ki T T
    Chi-Chi T F
    The possibility which is mentioned above satisfies the conditions. So, Ti-Ti passed the goods, Ki-Ki created diversion and Chi-Chi took goods out of shop. So answer is option 3.
  2. Which of these statements is correct?
    1. Chi-Chi created the diversion.
    2. Ti-Ti took the goods out of the shop.
    3. Chi-Chi passed the goods.
    4. Ti-Ti passed the goods.
    Sol: Option 4
    Solution: Let us assume that Ti – Ti speaks the truth. Then as his both statements are true, so we get the arrangement as Chi - Chi passed the goods, Ki-Ki created diversion and Ti-Ti took goods out of shop.
    But when this arrangement is validated as per the statement, we find that there is one Truth Teller, one Liar and one alternator. This scenario violates the given condition that there is one truth teller and two alternators. So our assumption that Ti – Ti is the truth teller is wrong.
    Assume that Ki-Ki speaks the truth. (F- False, T- True). Then we get the following table:
      1st 2nd
    Ti-Ti F T
    Ki-Ki T T
    Chi-Chi T F
    The possibility which is mentioned above satisfies the conditions. So, Ti-Ti passed the goods, Ki-Ki created diversion and Chi-Chi took goods out of shop. So answer is option 4.
  3. On an Island, three types of tribes live- Saca, Jhav and Lobe. Sacas’ always tell the truth, Jhavs’ always lie and Lobes’ tell the truth and lie alternating (they can tell truth first or lie first). Three persons (of different tribes) from this Island give these statements.
    GABE: UCKO is of Sacas tribe; I am of Lobe tribe
    BORRIS: GABE is of Jhavs tribe; I am of Sacas Tribe
    UCKO: BORRIS is of Jhavs tribe; I am of Lobe tribe.
    GABE belongs to which tribe?
    1. Sacas
    2. Jhavs
    3. Lobe
    4. Either 1 or 3
    Sol: Option 2
    Solution: If we assume Gabe is of Saca tribe, his both statements should be true. But one of his statements that Ucko is of Saca tribe should be wrong as there is only one Saca tribe person.
    Now assume Borris is of Saca tribe. His second statement is obviously true and his first statement indicates that Gabe is of Jhav type which implies that Ucko is of Lobe type.
    Now checking of the truthfulness of the statements of Gabe and Ucko, we get Gabe's both the statements are wrong and Ucko's one statements is correct and one is wrong. So Gabe belongs to Jhav tribe.
DIRECTIONS for questions 6 – 7: Consider the following statements and answer the questions that follow.
Chetan, Mohan and Thomas participated in a race and one of them won the race. They belong to three different communities - Saki, Noro and Carro. Sakis always speak the truth, Noros always lie and Carros tell the truth and lie alternatively. (Each of Chetan, Mohan and Thomas belongs to one community.) After the race they gave these statements.
Chetan:
  1. I would have won the race if Thomas had not obstructed me at the last moment.
  2. Thomas always speaks the truth.
Mohan:
  1. Chetan won the race.
  2. Thomas is not a Noro.
Thomas:
  1. I hadn’t obstructed Chetan at the last moment.
  2. Mohan won the race.
  1. Thomas belongs to which community?
    1. Saki
    2. Noro
    3. Carro
    4. Either 2 or 3
    Sol: Option 3
    Solution: Assume Mohan is a truth teller (So he is a Saki). Then Chetan is the winner and Thomas is Carro (Alternator) which implies Chetan is a liar (Noro).
    If we check the truthfulness of the Chetan, we get that both his statements are wrong and Thomas's one statement is wrong. So Thomas belongs to Carro and Chetan won the race.
  2. Who won the race?
    1. Mohan
    2. Thomas
    3. Chetan
    4. Data Inadequate
    Sol: Option 3
    Solution:Assume Mohan is a truth teller (So he is a Saki). Then Chetan is the winner and Thomas is Carro (Alternator) which implies Chetan is a liarr (Noro).
    If we check the truthfulness of the Chetan, we get that both his statements are wrong and Thomas's one statement is wrong. So Thomas belongs to Carro and Chetan won the race.
  3. While searching for a Painter, Ali met three locals - Raj, Rajan and Roy - who always gave two replies to any question. Among them one is a truth teller, one is a liar and one is an alternator. When Ali asked them, "Who among you is the painter?", their replies were :
    Raj:
    I am the Painter
    Rajan is a liar
    Rajan:
    I am the Painter
    Roy is a liar
    Roy:
    Rajan is the Painter.
    Raj is a liar.
    NMAT Rigistration India
    1. Raj
    2. Rajan
    3. Roy
    4. Either 2 or 3
    Sol: Option 2
    Solution:Let's suppose Raj is a truth teller. Then according to Raj, Rajan is a liar. Hence Roy would be alternator i.e. one of his statements should be true and others should be false. But in this case, both of his statements are false. Hence Raj is not the truth teller.
    If Roy is truth teller, then according to him, Raj is a liar and Rajan is a painter and hence Rajan is an alternator. And we can verify that Rajan's first statement is true and second is false. Hence this assumption is true and Rajan is the painter.