🔁 Boolean Equivalence — A ⊕ B ≡ A ⊙ B'

🧠 Core Insight

• A XOR B (A ⊕ B) detects difference between A and B.
• A XNOR B′ (A ⊙ B′) detects sameness between A and the inverted B.
• Since B is flipped, the sameness check in XNOR now aligns with the difference check in XOR.

🔍 Truth Table Comparison

✅ The outputs of A ⊕ B and A ⊙ B′ match perfectly.

🔧 Algebraic Proof

Start with:

A ⊕ B = A·B̅ + A̅·B