here 4 NOR gates required

$\left ( \left ( X_{1}+X_{3} \right )'+\left ( X_{2}+X_{3} \right )'+\left ( X_{4}+X_{3} \right )' \right )'$

$\left ( \left ( X_{1}+X_{3} \right )'+\left ( X_{2}+X_{3} \right )'+\left ( X_{4}+X_{3} \right )' \right )'$

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