Are these the same term? Intuition tells me they are the same, but can we derive them one from other?

Question

D+GI vs D+D'GI, are they the sam term ? I even draw a true table for it. But how can we do it with boolean algebra? Adding a truth table.

Where D+GI is the POS from the table and D+D'GI is the SOP from the table. I believe they should be the same.

No they are not sam. If you have a true table then please add it into your question. — Transistor, Sep 30 '21 at 18:20
Have a look at this PDF: http://www.gti.bh/Library/assets/part2-s9luuiwx.pdf. They have a proof that A+A'B=A+B, but I consider the truth table to be a better proof on its own. — Justin, Sep 30 '21 at 18:23

user28910 · Accepted Answer · 2021-09-30T18:32:18.137

1

D + GI

D + (D + D') GI

D + DGI + D'GI

D (1 + GI) + D'GI

D (1) + D'GI

D + D'GI

edited Sep 30 '21 at 18:32

answered Sep 30 '21 at 18:28

user28910

Wait: shoud D+1+D'GI not always be 1 (if + is the OR operator) – JvO Sep 30 '21 at 18:29
What's the point of the D (1 + GI) + D'GI step, if DGI simplifies to 1? You might as well remove it – caird coinheringaahing Sep 30 '21 at 18:30
@JvO Oops. Fixed it – user28910 Sep 30 '21 at 18:33

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