If you have a boolean function with only "true" and "don't care" (no false) outcomes, how would you write the equation?

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In my homework I came across a situation where I had a Karnaugh map that only contained don't cares and trues. Since there are no false outputs possible, it seems like the equation would just be f(x,y,z) = TRUE. Am I right or am I missing something?

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That sounds about right to me - your specification is basically for a circuit that outputs 1 or anything, so outputting 1 is correct.