Boolean function equivalent

Question

The following Boolean function equivalent to. F(A,B,C,D) = PI(1,3,5,7,13,15)

a)BD' + ACD' b)BD'+ACD+ABC'D c)(B+D')(A+C+D') d)(A+D')(B'+D')

I wrote down the truth table for 4 input. I tries simplifying the SOP expression but it is not matching with any of the options.

Answer 1

There is no match. You are right.

I am first looking at the input combinations which are not dependent on the order of inputs:

If all four inputs are true (= minterm 15), expressions a) and d) return false and are thus ruled-out.

All inputs false (= minterm 0) is not part of the expression but is covered by c). Therefore, it can't be c)

The numbering of minterms $0..15$ depends on the column order of the input variables in the truth table. Usually, the left-most input has the highest weight and the right-most variable the lowest weight.

Assuming variable weights of A=8, B=4, C=2 and D=1: Term BD' covers minterms $1,3,9,11$ which are not all part of the expression

Variable weights A=1, B=2, C=4 and D=8: Term BD' now covers minterms $2,3,6,7$ which are also not completely covered by the expression.