# Relation between Sum of Min terms and product of max terms

My professor taught in class that the complement of sum of min terms of an expression is equal to the product of maxterms of the same. I.e, (Sum of min terms)' = (product of maxterms) How is this possible?

• What makes you think it is not possible? Have you tried doing the Boolean algebra on a few examples? Are you familiar with DeMorgan's theorem? – Elliot Alderson Jan 26 at 19:25
• @Elliot Alderson Lets look at a two input XOR gate. The SOM exp would be A'B + AB' and the POM will be (A + B)(A' + B'). How are they the complement of each other? – Le Connoisseur Jan 26 at 19:35
• OK, I see the confusion. The POM as you have written it is not the complement of the function it is the same as the SOM. The POM for the complement of the XOR function is F'=(A'+B)(A+B') – Elliot Alderson Jan 26 at 20:08
• Yeah, so shouldn't the SOM and POM of the same function have the same outcomes? Because I want to write the expression for XOR function in terms of POS. I can't just complement the SOM once and get the POS of the XOR function right? – Le Connoisseur Jan 26 at 20:56
• Yes, and they do. A'B+AB' = (A+B)(A'+B') Also, (A'B+AB')'=(A+B')(A'+B) – Elliot Alderson Jan 26 at 21:00