Fallacy!

Algebra Level 4

Let $f:\{x,y,z\} \rightarrow \{a,b,c\}$ is an injective function.

It is known that only one of the following statements is correct and rest are false:

1). $f(x) \ne b$

2). $f(y) =b$

3). $f(z) \ne a$

What is $f(x)$ ?

c

a

b \text{ or } c

c \text{ or } a

\text{any of } a,b,c

a \text{ or } b

b

1 solution

Amiel Chua
May 15, 2015

1.) If $f(x) \ne b$ is true, then

$f(x) \ne b$

$f(y) \ne b$

$f(z) = a$

this cannot happen because there will be no place for $b$ , thus 1 is false.

2.) If $f(y) = b$ is true, then

$f(x) = b$

$f(y) = b$

$f(z) = a$

which cannot happen because both $x$ and $y$ will be both equal to $b$ . With 1 and 2 being false it leaves us only one choice.

3.) If $f(z) \neq a$ is true, then

$f(x) = b$

$f(y) \neq b$

$f(z) \neq a$

$\boxed{f(x) = b}$ , $f(y) = a$ , $f(z) = c$ . it's a perfect fit.