The circuit shown in the following figure realizes the function Fig

First, analyze the top branch: Inputs A and B go into a NOR gate producing (A+B)'. This output is fed into another NOR gate with input C, resulting in ((A+B)' + C)'. Next, analyze the bottom branch: Inputs D and E go into a NOR gate producing (D+E)'. This signal is then inverted to yield D+E.

Finally, these two branch outputs enter a NOR gate. The final expression is [ ((A+B)' + C)' + (D+E) ]'. Applying De Morgan's Law, the complement of the sum is the product of the complements. The first term simplifies to ((A+B)' + C) and the second term becomes D'E'. The final simplified function is ((A+B)' + C)(D'E').