Logical Reasoning section in Common Admission Test (CAT) carries a couple of questions on binary logic. The application of this logic is more in finding out the truthfulness in the statements made.
In a binary logic problem, we have people who either speak a true statement or a false statement. These people are divided into three categories:
- Truth-teller: This person will always speak the truth. All the statements made by this person are true.
- Liar: This person will always tell a lie. All statements made by this person are false.
- Alternator: This person always alternates between the truth and the lie. If first statement of this person is true, then second will be false, third will be true and so on. Similarly, if first statement made by this person is false, then second will be true, third will be false and so on. There is no particular number of true statements or false statements made by this person but order is always TRUE-FALSE-TRUE- or FALSE-TRUE-FALSE.
Binary logic questions are all about making some assumptions (kind of assumptions are described later). These assumptions may give rise to some contradictions which are the indicators that our assumptions are wrong. If for any assumption we do not get even a single contradiction, then that is the solution for the given binary logic problem.
The binary logic is a set of rules for dealing with propositions that must be either true or false. There are three operations common to all binary logic systems, AND, OR, and NOT. In addition to that, many logic systems add the operations IF . . . THEN, IF AND ONLY IF, and EOR. Notations vary greatly, so it is important to remain consistent in how one writes out binary logic.
Relevance to CAT:
The advantage of binary logic is that it provides a set of formal rules that can be used to test statements (propositions) for contradictions. Out of the ten questions in Logical Reasoning, one may expect to find two questions based on Binary Logic. The application of this logic is more in finding out the truthfulness in the statements made. It allows for statements that are neither true nor false and/or statements with degrees of truthfulness.
How to crack the questions:
Two types of questions based on Binary logic can be found in the Logical Reasoning section. The aspirant has to match the two logic propositions in each question.
Question Type – 1:
Two statements by each of the three persons are made in this type. One of the statements has got to be true and other is false. Now, one has to consider the two Propositions to arrive at the right answer.
- The statement logic of the contents stated within
- The ingredients i.e. the fact- one is true other will be naturally false or vice versa.
Question Type – 2:
Two types of persons are found in this type of question.
- Those who always speak the truth
- Those who always tell a lie
Methods to solve:
With the help of some statements made by these people we might be able to identify them without any assumption. Here is a list of 4 statements which one must always look out for to make the task easier. If any one of these is made by any person, then we can categorize them as explained below.
- I am a liar:
Consider if a truth-teller says, “I am a liar”, which is a lie as a truth-teller can only say, “I am a truth-teller”. Hence, we can conclude that the person who said “I am a liar” is not the truth-teller.
Similarly, if a liar says that he/she is a liar then that statement will be true but the liar will always speak the lie. None of the statements made by him/her can be true. We can conclude this statement cannot be made by a liar.
The only category of person who can speak this statement can be the alternator. He can alternate between the truth and the lie. Since, he/she is not a liar but he/she can still make a false statement, alternator is the only category of people who can make the statement, “I am a liar”. The statement in itself will be a lie. This gives us another hint that the statement proceeding and the statement preceding this statement will always be a true.
- I am not a truth teller:
Similar to the explanation above, a truth-teller can never make this statement because if he/she makes this statement then it will be a lie which contradicts the fact that a truth-teller always speaks the truth.
If the liar makes the above statement, then it will be the truth for him which again contradicts the fact that a liar will always lie. Hence, a liar cannot make this statement.
The alternator can say, “I am not a truth-teller”, as he can say either the truth or the lie. This statement will be a true statement for him, which gives us another hint that the statements preceding and proceeding this statement are the lie.
- I am an alternator:
A truth-teller cannot make this statement as this statement will be a lie for him which conflicts the fact of the truth-teller.
A liar can make this statement as this statement will be a lie for him/her.
An alternator can also make this statement and this will be the truth for the alternator.
We can conclude that this statement can be made by the liar or the alternator.
- I am not an alternator:
Similar to the above statement, a liar will not make this statement.
A truth-teller can make this statement.
An alternator can make this statement and this time it will be the lie for him/her.
To summarize the above explanations:
| Statement |
Made by |
Truth or lie |
| I am a liar |
Alternator |
Lie |
| I am not a truth-teller |
Alternator |
Truth |
| I am an alternator |
Liar or alternator |
Lie for liar, truth for alternator |
| I am not an alternator |
Truth-teller or alternator |
Lie for alternator, truth for truth-teller |
Note: In some cases, where none of the four statements as mentioned above was made by anyone, we will use the assumption-iteration method (or the case method). In this method we will assume the first person as the truth-teller and based on his statements we will try to find contradictions that may arise due to the statements made by others.
