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Express F in SOP and POS form

With its truth table, express F in SOP and POS form $$F(A,B,C) = \sum m(0,3,5,7)$$

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Since, there are 3 variables - A, B, C, so the number of select lines = 3.

Therefore, number of data inputs = $2^3=8$

Therefore, 8:1 MUX is needed.

Sum of Product (SOP)

For SOP, connect all the minterm inputs i.e 0,3,5,7 to logic 1 and rest of the input lines to logic 0.

enter image description here

The truth table is as shown -

Input Line A B C Output F
0 0 0 0 1
1 0 0 1 0
2 0 1 0 0
3 0 1 1 1
4 1 0 0 0
5 1 0 1 1
6 1 1 0 0
7 1 1 1 1

Product of Sum (POS)

For POS, connect all the maxterm inputs i.e 0,3,5,7 to logic 0 and rest of the input lines to logic 1.

enter image description here

The truth table is as shown -

Input Line A B C Output F
0 0 0 0 0
1 0 0 1 1
2 0 1 0 1
3 0 1 1 0
4 1 0 0 1
5 1 0 1 0
6 1 1 0 1
7 1 1 1 0
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