Find the essential prime implicants

Question

Given F=xy+z

What is /are the essential prime implicants of F?

a) xy

b) z

c) either a or b

d) Both a and b

Comments

Given solution: [[ Please clarify whether this is the right way to solve]]

If a prime implicant includes a minterm that is not included in any other prime implicant, then that prime implicant is essential

Check in order:

• xy--> xyz,xyz’ are minterms produced by xy. These minterms are not produced by any other prime implicants so far. xy is essential
• z --> xyz, xyz, xyz’, x’yz, xy’z, x’y’z are mintrems produced by z. These minterms are already produced by xy. Hence z is not essential
• If z was checked first, z is essential and xy is not

Hence solution is either a or b

Answer 1

2 pi (1,3,5,7)  for z nd (6,7) for xy both r epi

Comments

Can you explain a little, plz..

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z --> xyz, xyz, xyz’, x’yz, xy’z, x’y’z are mintrems produced by z. These minterms are already produced by xy. Hence z is not essential
if atleast 1 minterm is not coverd by other pi then it is epi

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So answer should be either xy or z not both.

Am I correct?

Answer 2

Option (D) is correct
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