Group 4

Mebers: Elloani Ross Pitogo

Canebin Gulbin

Charles Chiong

John Leroy Damulo

Sean Michael Fabregas

THE CASE OF THE STOLEN SMARTPHONES

Scenario:

During an investigation into the mysterious disappearance of students’ smartphones inside the campus,

the following statements were made by the prime suspects:

Canebin: I wouldn’t steal any smartphones unless Leroy helped me.

Charles: Me? Steal smartphones? Of course not! I’m too honest for that. Besides, I can afford to

buy as many as I want!

Leroy: If I stole it, then either Canebin or Sean was in too.

Sean: Neither Leroy nor I were involved.

Given that exactly one of the four suspect is lying and exactly two of them were involved in the theft, who

are the thieves and who is lying?

Solution:

1. Symbolize the alternative propositions.

Let:

A Canebin stole the smartphones.

B Charles stole the smartphones.

C Leroy stole the smartphones.

D Sean stole the smartphones.

2. Put the statements of the suspects into an equation.

Canebin’s statemen = -A v (A ^ C)

Charles’ statement = -B

Leroy’s statement = C --> (A v B)

Sean’s statement = -(C v D)

3. Construct a truth table.

A B C D -A (A ^ C) -A v (A ^ C) -B (A v B) C --> (A v B) (C v D) -(C v D)

0 0 0 0 1 0 1 1 0 1 0 1

0 0 0 1 1 0 1 1 0 1 1 0

0 0 1 0 1 0 1 1 0 0 1 0

0 0 1 1 1 0 1 1 0 0 1 0

0 1 0 0 1 0 1 0 1 1 0 1

0 1 0 1 1 0 1 0 1 1 1 0

0 1 1 0 1 0 1 0 1 1 1 0

0 1 1 1 1 0 1 0 1 1 1 0

1 0 0 0 0 0 0 1 1 1 0 1

1 0 0 1 0 0 0 1 1 1 1 0

1 0 1 0 0 1 1 1 1 1 1 0

1 0 1 1 0 1 1 1 1 1 1 0

1 1 0 0 0 0 0 0 1 1 0 1

1 1 0 1 0 0 0 0 1 1 1 0

1 1 1 0 0 1 1 0 1 1 1 0

1 1 1 1 0 1 1 0 1 1 1 0

4. Look at the scenario again and understand. Understanding it is the key. Make a conclusion afterwards

and check if your conclusion makes logical sense.

From the fact that one is lying, therefore three of the equations must be true (1) and one must

be false (0).

That leads us to five options: rows 2, 5, 9, 11 and 12 have only one false (0) under the columns

of the four equations (orange).

From the fact that two them are thieves, therefore one of the five rows must have two trues (1)

and two false (0) under the columns of the four propositions (green).

That leaves us only row 11.

As a conclusion, we can say that:

Canebin and Leroy stole the smartphones.

Sean is the liar.