Completing the implicant entries is optional. If there are none, leave the entry

blank. Find the minimum Sum of Products for the given function.

$F(a,b,c,d,e)=Em(1,3,{?}^7,16,17,19,20,21,23,24,25,28,29,30,31)+$

$d(2,13,14,15)$

$a=0$

$d\frac{e}{b}c00,01,11,10de$

Karnaugh map $is$ optional.

You may request that $itbe$

checked but $no$ corrections

$($Optional$)$Enter the essential prime implicants, separated by commas. $(2$ terms$)$

$($Optional$)$ Enter the prime implicants, separated by commas. $(8$ terms$)$

Check Implicants Answers must be in sum of products form.

Enter at least $3$ solutions, one per entry box.

All provided solutions must be correct.

$F=$

$F=$

$F=$

$F=$