Define the first injective function, f1: A B.

To write two injective functions from set $A = \{x,y,z\}$ to set $B = \{1,2,3,4\}$, we need to ensure that each element in $A$ maps to a unique element in $B$.

Step 1: Define the first injective function, $f_1: A \to B$. We can map the elements of $A$ to distinct elements of $B$. $f_1(x) = 1$ $f_1(y) = 2$ $f_1(z) = 3$ This function is injective because each element in $A$ maps to a different element in $B$.

Step 2: Define the second injective function, $f_2: A \to B$. To make it different from $f_1$, we can change one or more of the mappings, ensuring it remains injective. $f_2(x) = 1$ $f_2(y) = 2$ $f_2(z) = 4$ This function is also injective because each element in $A$ maps to a different element in $B$.

The two injective functions are:

• $f_1: A \to B$ defined as $f_1(x) = 1$, $f_1(y) = 2$, $f_1(z) = 3$.
• $f_2: A \to B$ defined as $f_2(x) = 1$, $f_2(y) = 2$, $f_2(z) = 4$.

These are just two examples; many other injective functions are possible.

The two injective functions are:

• $\boxed{f_1 = \{(x,1), (y,2), (z,3)\}}$
• $\boxed{f_2 = \{(x,1), (y,2), (z,4)\}}$

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