Implement XNOR using NAND gates ?

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To implement XOR using NAND gates, a minimum of 10 NAND gates is calculated, including gates for inverting inputs and creating AND and OR functions. However, the question posed involves finding a solution using only 3, 4, 5, or 6 NAND gates. It is suggested that three NAND gates can be combined to achieve the necessary functions for XOR. The discussion also references additional resources, like Wikipedia, for further insights. The challenge remains to derive the XNOR function efficiently using fewer gates.
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what is minimum number of NAND gates to implement XOR?
i thought it in this way .first i found how many NAND gates are need to to implement XOR .
if the two input it 'A' nd 'B'
then
XOR function =A'B+AB'
so i need two NAND gates to invert A and B
then for two AND gates i need another 4 NAND gates as each AND gate need 2 NAND gates .
then for final OR gate i need another 3 NAND gate .
so this will give the XOR function .To make it XNOR i need another NAND gate

so total number of NAND gates=2+4+3+1=10

but in my MCQ question it has only
a)3 b)4 c)5 d)6

i don't how to implement XNOR in one of above answers ,totally by NAND gates .can somebody help me ?
Thanks !
 
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Three NAND gates can be combined to produce the double AND plus OR function. The rest are just those required for the invert operations.
 
ok thnaks !and i found some good ideas from wikepedia also !
 

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