BINARY LOGIC QUESTION—P ATTERNS

Type 1

In this question type, three persons speak two statements each—one of which is true, the other is false.

The two logic streams to be considered are:

1. The logic of the Statements, i.e., the logic of what is said within the statements.

2. The logic of the Basic Conditions, i.e., the logic of the fact that if one sentence is taken as true, the other will be false automatically.

The process of solving these questions is best illustrated through an example.

Gauri Islands is the name of an island. The inhabitants of this island always answer any question with two sentences. One of which is always true and the other always false.

Milly, Silly and Dilly are the three daughters of the chief whip of this island. Out of them, two are minor and one is of a marriageable age. You have been caught as an intruder on the island and you have two options given by the chief whip: identify his daughter who is of marriageable age. If you do so, you can have the privilege of marrying her and becoming the new chief whip in the future. On the other hand, if you cannot, you will be executed. Only Silly has dentures in her teeth. On questioning the three daughters, these are the answers you get:

Milly: “I am shorter than Silly. The girl of marriageable age has dentures in her teeth.” Silly: “I am shorter than Milly. Dilly is the one who is of a marriageable age.”

Dilly: The girl of marriageable age is amongst the three of us. I am of a marriageable age.”

Who is the girl of marriageable age?

(a) (b) Dolly

Milly

(c) Silly(d) Can’t say

In the above question, you should see that, the first statement of Dilly has to be correct (By Logic of the statement—If you evaluate what the statement is saying, it is clear that it has to be true. It can be easily understood that the girl of marriageable age is amongst the three of the girls.)

In this case, if this statement is true, then Dilly’s second statement is automatically false. Further, since Dilly’s second statement is false, Silly’s second statement will also be false. (By evaluating the sentence logic—as both these statements are saying the same thing.) Hence, Silly’s first statement will be true (Basic Condition logic) and hence further, Milly’s first statement will be false (It is saying the opposite of Silly’s true first statement—Statement Logic). Hence, Milly’s second statement has to be true. Hence, Silly has to be the one of marriageable age.