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I'm trying to understand if it's possible to Implement boolean function with 3 inputs using only mux 4 to 1 and inverter. As far as I understand I can put in the selectors the first 2 variables to select between the 4 options. then I have another variable which I can connect to the 4 options (00,01,10,11) but I can't solve it to make sure it will suffice any 3 variables function.

I would like to know how to approach this kind of questions, how to "prove" such things?

Thanks.

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It is possible to make any boolean function f(a,b,c) using a 4:1 mux and an inverter

With the inverter make ~c

Connect a and b to the mux address lines.

Connect each mux data input to the one of 0,1,c,or ~c as appropriate.

The mux output has your function result.

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