Prove that X-OR is complement of X-NOR with the help of a truth table

To prove that XOR (⊕) is the complement of XNOR (⊙), we will construct a truth table for both operations.

A	B	A ⊕ B (XOR)	A ⊙ B (XNOR)
0	0	0	1
0	1	1	0
1	0	1	0
1	1	0	1

From the table, we see that:

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When

𝐴⊕𝐵=0

then

𝐴⊙𝐵=1

When

𝐴⊕𝐵=1

then

𝐴⊙𝐵=0

Thus, XOR and XNOR are complements of each other. ✅