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For the following figure:

NOR gate circuit

what is the ouput if
a) both inputs are low
b) if one input is high and one low
c) does the circuit act like an OR or AND gate

I understand that the output for the first part of the circuit is 1 if both inputs are low only. I am confused about the connection between the first and second part of the circuit.

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    The second circuit just has the same input on both ports, that is, it is either both zero or both one. – 2017-02-06
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    The output of the first gate is connected to both inputs of the second gate. Where exactly is your confusion? – 2017-02-06
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    I just wanted to reaffirm that was the case @celtschk. So if the output is 1, then that is the input for both a and b in the next part of the circuit? – 2017-02-06
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    @julian: Exactly. – 2017-02-06
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    Hint: think of the first $NOR$ as an $OR$ followed by a $NOT$. Then $Y$ is $A\;OR\;B$ negated twice. – 2017-02-06

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By low, I assume you mean zero ? A nor gate gives one when both inputs are zero & gives zero in the 3 other possible cases. So the answer to a) is high & b)is low. The output from the first NOR gate will be $A$ NOR $B$, this will then be the inputs for both sides of the next NOR gate & so a formula for Y is given by \begin{eqnarray*} Y = (A \ NOR\ B) \ NOR\ (A \ NOR\ B) \end{eqnarray*} Now make a truth table for this & you will be able to rapidly conclude that it is the same as an OR gate.