Binary

Purpose-driven system (built from gates)	Core gate(s)	Why it’s helpful / real-world impact
Secure door lock — opens only when every credential is valid (badge AND PIN,[ AND ])	AND	Raises physical security; reduces unauthorized entry by demanding multiple independent proofs of identity.
Burglar alarm — sounds if any sensor trips (window, motion, glass-break, OR)	OR	Improves safety by turning one of many possible intrusions into a single, timely alert.
Automatic night light — lamp turns on when it’s dark AND someone is present (light sensor NOT + AND with PIR)	NOT + AND	Saves energy and extends bulb life while still providing illumination only when it’s actually useful.
Emergency-stop latch — machine runs while enable-switch is 1 AND no fault is present (NOT fault AND run)	AND + NOT	Prevents equipment damage/injury by forcing the motor off the instant a fault line goes high.
Majority-vote controller — critical system keeps working if ≥ 2 of 3 subsystems agree (3-input majority)	combinations of AND/OR	Provides fault-tolerance in aerospace/medical devices; a single faulty sensor can’t bring the system down.
Parity / XOR error-checker — detects flipped bits on data links	XOR	Increases data reliability; corrupted packets are caught before they cause crashes or wrong results.
Adders, multiplexers & registers (building blocks of CPUs)	AND, OR, XOR, NOT	Deliver the speed-and-power advantages of digital computing to everything from phones to pacemakers.

The circuit is true when:

X AND Y are both 1 OR

Z is 1 (regardless of X and Y).

That’s literally the expression

( 𝑋 ∧ 𝑌 ) ∨ 𝑍 (X∧Y)∨Z Answer: A. (X AND Y) OR Z

(The other options either evaluate the OR/AND in the wrong order or negate the wrong part.)

def secure_entry_system(keycard, pin, voice):
    """
    Returns 1 (granted) only if *all three* credentials are present.
    Each argument should be 0 or 1.
    """
    def AND3(a, b, c):
        return a & b & c  # 3-input AND logic using bitwise-AND
    
    return AND3(keycard, pin, voice)

# --- Test cases ---
print(secure_entry_system(1, 1, 1))  # ➜ 1  (Access granted)
print(secure_entry_system(1, 0, 1))  # ➜ 0  (Denied: wrong PIN)
print(secure_entry_system(0, 1, 1))  # ➜ 0  (Denied: no keycard)
print(secure_entry_system(1, 1, 0))  # ➜ 0  (Denied: voice mismatch)