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2 Answers

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a function is called self dual if it does not contain mututally exclusive term 
 

decimal  binary
0 000
1 001
4 100
6 110

here in the above table blue color marked enteries are mutually exclusive terms so
answer D) option 

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D)

for A)

Dual of  F(A,B,C)=$\sum m(3,5,6,7) =\prod m(0,1,2,4)$

$\prod m(0,1,2,4) =\sum m(3,5,6,7)$

$\sum m(3,5,6,7)=\sum m(3,5,6,7)$

For B)

Dual of  F(A,B,C)=$\sum m(1,2,4,7) =\prod m(0,3,5,6)$

$\prod m(7,6,3,1) =\sum m(1,2,4,7)$

$\sum m(1,2,4,7)=\sum m(1,2,4,7)$

For C)

Dual of  F(A,B,C)=$\sum m(0,2,4,6) =\prod m(1,3,7,6)$

$\prod m(1,3,7,6)=\sum m(0,2,4,6)$

$\sum m(0,2,4,6)= \sum m(0,2,4,6)$

for D)

 Dual of  F(A,B,C)=$\sum m(0,1,4,6) =\prod m(7,6,3,1)$

$\prod m(7,6,3,1) =\sum m(0,2,4,5)$

$\sum m(0,1,4,6)\neq \sum m(0,2,4,5)$

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