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The definition says that we can use a don't care as either 1 or 0. It seems that if we consider a don't care as 1, we can't consider it as 0 while computing product of sum from the same k-map. Is it true? Any explanation on this stating the actual significance of don't care would be highly appreciated.

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    \$\begingroup\$ You can, but note, that the resulting expressions won't be equivalent. They will be equivalent for the non-don't care combinations. \$\endgroup\$
    – Eugene Sh.
    Commented Jan 13, 2016 at 19:01

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Don't care means what it says, we don't care what the output is under that combination of inputs.

So if we treat it as a 1 when doing SOP and a 0 when doing POS we will end up with two results which are not equivilent to each other but which are both valid soloutions to the original problem described by the k-map.

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