Simplify the following Boolean expression. E(E + F) + DE + D(E + F)
2021
Simplify the following Boolean expression.
E(E + F) + DE + D(E + F)
- A.
E + DF
- B.
F + DE
- C.
D + EF
- D.
D + E + F
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Correct answer: A
Simplify E(E + F) + DE + D(E + F) step by step using Boolean algebra.
1) Expand E(E + F) = E·E + E·F = E + E·F (since E·E = E, idempotent law).
2) E + E·F = E (absorption law). So the first term reduces to E.
3) Expand D(E + F) = D·E + D·F.
4) Now combine all terms: E + DE + (DE + DF) = E + DE + DF.
5) E + DE = E·(1 + D) = E (absorption law, since 1 + D = 1).
6) The expression reduces to E + DF.
Hence the simplified form is E + DF.