
(c) Output of gate-1,
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Output of gate-2,
Output of gate 3 $Y_{1} = \overline{A}$
$Y_{2} = \overline{B}$
$Y = \overline{Y_{1} + Y_{2}} = \overline{\overline{A} + \overline{B}} = \overline{\overline{AB}} = AB$
which is the output of AND gate.