The image contains a relay-contact scheme. I will analyze the circuit step by step to determine the logic function $f$ based on the inputs $x$, $y$, and $z$.

Step-by-Step Analysis

1. Input Components:

   • Inputs $x$, $y$, and $z$ control the circuit.

2. Logic Gates:

   • The circuit contains basic logical components: AND ($\&$), OR ($+$), and equality ($=$) gates.
   • A logical negation or complement is applied to one input.

3. Path Analysis:

   • Trace the paths and interactions of $x, y, z$, through each gate step by step.

Let’s derive the function $f$:

• $x$: Appears as input to an AND gate. After analyzing the relay-contact scheme in the image, here's a detailed breakdown of the logical structure and the resulting function $f$:

Key Observations

1. Inputs:

   • Inputs are $x$, $y$, and $z$.

2. Logic Gates:

   • Two AND gates ($\&$).
   • One OR gate.
   • One equality comparison gate ($=$).
   • Input negation (denoted by a small circle) is applied to certain signals.

3. Connections:

   • $y$ and $z$ are fed into the equality gate ($=$), which outputs $1$ if $y = z$.
   • $x$ directly interacts with these outputs through additional AND gates.
   • The outputs of the gates are combined logically to produce $f$.

Step-by-Step Logical Expression Derivation

Step 1: Equality Gate ($y = z$):

• The equality gate outputs $1$ if $y = z$, so its output can be written as: $\text{Equality Output: } E = (y \cdot z') + (y' \cdot z).$

Step 2: First AND Gate:

• One AND gate takes the inputs $x$ and $E$: $A_1 = x \cdot E.$ Substituting $E$: $A_1 = x \cdot [(y \cdot z') + (y' \cdot z)].$

Step 3: Second AND Gate:

• Another AND gate directly combines $x$ with $y$: $A_2 = x \cdot y.$

Step 4: OR Gate:

• The final output $f$ is the OR of the two AND gate outputs: $f = A_1 + A_2.$ Substituting $A_1$ and $A_2$: $f = [x \cdot ((y \cdot z') + (y' \cdot z))] + (x \cdot y).$

Step 5: Simplify $f$:

• Distribute and simplify: $f = (x \cdot y \cdot z') + (x \cdot y' \cdot z) + (x \cdot y).$

Final Logic Function:

The resulting logic function is: $f = x \cdot y + x \cdot y' \cdot z + x \cdot y \cdot z'.$

This is the simplified expression for the relay-contact circuit.

Do you have questions or need further details?

Related Questions:

1. What does the equality gate specifically do in such circuits?
2. Can the logic function $f$ be represented using Karnaugh maps?
3. How would the circuit behave for specific input combinations of $x, y, z$?
4. Can we design an equivalent digital circuit for this relay-contact scheme?
5. What practical applications exist for such relay circuits?

Tip: To validate logic circuits, use truth tables or simulation software to check your derived expression.