Classification of persons in Binary Logic:
1. Truth
Teller: Someone who always tells the truth (all statements made has to
be assumed to be true).
2. Liar:
Someone who always lies (all statements made has to be assumed to be false).
3. Alternator:
Someone who alternately lies and tells the truth in any order (any two
statements in a row will consist of exactly one true and one false statement).
Some typical statements and their
implications:
i) I am a liar – no liar and truth
teller will ever make this statement as it would end up becoming a true and
false statement respectively. Hence if such a statement is given, we can
conclude that the speaker is definitely an Alternator
and the given statement is false.
Also statements immediately preceding and following it from the same speaker will
be true statements.
ii) I am
not a truth teller – like previous example this statement too can only
be made by an Alternator and the
nature of the statement shall be true.
Also statements immediately preceding and following it from the same speaker
will be false statements.
iii) I am
an alternator – this can either be a true statement of an Alternator or a false statement of a Liar. In both cases the immediately preceding
and following statements of the same speaker will be false.
iv) I am
not an alternator – this can be a false
statement of an Alternator or a true
statement of a Truth Teller. In both cases the immediately preceding and following
statements of the same speaker will be true.
In case one of the above
types of statements is given, then one can start with them and work out few
definitely correct/false statements which shall allow solving the set (eg #1).
In the absence of such direct clues, one has to work out different
possibilities to get to the answer (eg #2).
#1.
Each of three friends A, B and C are fond of exactly one of the three fruits –
apple, banana and orange with no two of them liking the same fruit. Also it is
known that each of them can be any of truth tellers, liars and alternators. On
being asked about their choice of fruits and talking patterns they gave the
following answers –
A:

I like apple

B does not like banana


C is an alternator


B:

I like orange

A is a liar


C likes apple


C:

I like banana

I am not an alternator


B likes apple

The person who likes
apple is a:
a) Truth Teller b) Liar
c) Alternator d) Either b or c
Sol.
After browsing through all statements made by A, B and C one can make out that
C’s second statement is either a true statement of a truth teller or a false
statement of an alternator – irrespective of which C’s first and third
statement have to be true. This gives us the following result –
A

Orange

B

Apple

C

Banana

Based on above we can
determine that A’s first statement is false and the second one is true. As the
three of them have to be one of truth tellers/liars/alternators; we can also
conclude that A is an alternator and her third statement is hence false (which
means C is not an alternator). This leads us to the conclusion that C is a
truth teller; thus C’s second statement also can be marked as true.
Hereafter when we
analyse B’s statements we realise they all are false; so B must be a liar. With
‘T’ standing for True and ‘F’ for False the nature of statements will be as
follows:
A:

I like apple

F

B does not like banana

T


C is an alternator

F


B:

I like orange

F

A is a liar

F


C likes apple

F


C:

I like banana

T

I am not an alternator

T


B likes apple

T

Ans.
Option b
#2.
There is exactly one truth teller, one liar and one alternator among A, B and
C. When asked about their identities they gave the following responses –
A:

I am a truth teller

C is an alternator


B is a liar


B:

I am not a liar

C is an alternator


A is a liar


C:

I am a truth teller

B is not a liar


A is not a truth
teller

Given that there are
only two males among them  the truth teller and liar; who is the only female
among the three?
a) A b) B
c) C d) Anyone of them
Sol.
Here as none of the statements can be termed as definitely true or false just
by reading them, we can start by assuming each one of them as truth teller
respectively.
Let A be the truth
teller in case 1, B in case 2 and C in case 3; then we get the following result
–
Case 1

Case 2

Case 3


A:

I am a truth teller

T

F

F

C is an alternator

T

T

F


B is a liar

T

F


B:

I am not a liar

F

T

T

C is an alternator

T

T

F


A is a liar

T

T


C:

I am a truth teller

T


B is not a liar

T


A is not a truth
teller

T

In case 1 as A’s all
statements are true, B is supposed to be a liar. However B’s second statement concurs
with that of A’s and becomes true. As a liar cannot make a true statement, case
1 is not correct.
Similarly case 2 can
also be eliminated as B is assumed to be a truth teller and his third statement
terms A as a liar. However they both make same second statements and the
assumed liar (A) ends up making a correct statement.
With case 1 & 2
eliminated we can conclude case 3 has to be correct which means C is the truth
teller. As per C, B is not a liar, hence B must be an alternator and also A
must be the liar.
As the female has to be
the alternator here, B is the only female among the three.
Ans.
Option b
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