To solve this relay-contact circuit diagram, let’s analyze it step by step. The circuit involves logical elements like AND, OR, and NOT gates combined with relay contacts. The inputs are labeled as $x$, $y$, and $z$, and the output is $f$.

Step-by-Step Analysis

1. Top Block (Relay Contact "1" connected to x, y, z):

   • The circuit reads the state of x, y, and z at the top.
   • The input is inverted at the output of the block (marked as 1), meaning this part implements a logical NOT operation.

   Expression for this part: $\overline{x}$.

2. Bottom AND Gate (x AND z):

   • This gate combines inputs $x$ and $z$ through a logical AND operation.

   Expression for this part: $x \cdot z$.

3. Equality Check (Middle Block "="):

   • This block checks for the equality condition between two signals, which are both inverted using NOT gates.
   • The inputs are likely to be $x$ and $y$, so this part outputs true if $x = y$.

   Expression for this part: $x = y$ (logical equivalence).

4. AND Gate (Right Side):

   • The outputs from the bottom AND gate ($x \cdot z$) and the equality block ($x = y$) are inputs to this AND gate.
   • This gate outputs the logical AND of those signals.

   Expression for this part: $(x \cdot z) \cdot (x = y)$.

5. Final OR Gate (Last Block "1"):

   • The inverted signal $\overline{x}$ is OR-ed with the AND gate result.

   Final Output Expression:
   $f = \overline{x} + \left[ (x \cdot z) \cdot (x = y) \right]$

Final Logical Expression

The output function $f$ is:
$f = \overline{x} + \left[ (x \cdot z) \cdot (x = y) \right]$

Explanation of Components

• $\overline{x}$: Inversion of input $x$.
• $x \cdot z$: Logical AND of $x$ and $z$.
• $x = y$: Logical equivalence between $x$ and $y$.

Let me know if you want further explanation of any steps, truth tables, or simplifications.
Here are 5 follow-up questions for deeper understanding:

1. What is the truth table for this circuit based on $x, y, z$?
2. Can the logical expression $f$ be simplified further using Boolean algebra?
3. What happens to the output $f$ if $x = 0$?
4. How does the circuit behave when $y \neq x$?
5. Can we design the same circuit using only NAND gates?

Tip:

Always simplify your final Boolean expression using Boolean algebra rules to reduce complexity.