The truth table for the given logic circuit is:

 

Correct Option - 3


Detailed Solution:

$\mathrm{C}=\stackrel{?}{\mathrm{A}\cdot \mathrm{B}}\cdot \stackrel{?}{\stackrel{?}{\mathrm{A}}\cdot \mathrm{B}}$

Using De-Morgan Theorem

$\mathrm{C}=\stackrel{?}{\mathrm{A}\cdot \mathrm{B}}\cdot \stackrel{?}{\stackrel{?}{\mathrm{A}}\cdot \mathrm{B}}$

$\mathrm{C}=\stackrel{?}{\mathrm{B}(\mathrm{A}+\stackrel{?}{\mathrm{A}})}=\stackrel{?}{\mathrm{B}}$

Therefore

 

<div class="photo-widget-full"><div class="figure"><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1756977234phpqSRJ5E.jpeg" alt="" width="234" height="99" loading="lazy"></picture></div></div><p><span contenteditable="false"> <math> <mi mathvariant="normal">C</mi> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">A</mi> <mo>⋅</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⋅</mo> <mover accent="true"> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⋅</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> </span></p><p>Using De-Morgan Theorem</p><p><span contenteditable="false"> <math> <mi mathvariant="normal">C</mi> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">A</mi> <mo>⋅</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⋅</mo> <mover accent="true"> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⋅</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> </span></p><p><span contenteditable="false"> <math> <mi mathvariant="normal">C</mi> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mo> (</mo> <mi mathvariant="normal">A</mi> <mo>+</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>)</mo> </mrow> </mrow> <mo>? </mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> </span></p><p>Therefore</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1756977326phpaLHbkV.jpeg" alt="" width="104" height="146" loading="lazy"></picture></div></div><p>&nbsp;</p></div></div>

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