The truth table for the following, logic circuit is

Correct Option - 1


Detailed Solution:

Using truth table of logic gates

$Y=\overline{\left(A\overline{B}\right)+\left(\overline{A}B\right)}=\overline{\left(\left(A\overline{B}\right)\right)}\overline{\left(\left(\overline{A}B\right)\right)}$

$Y=\left(\overline{A}+\overline{B}\right)\left(\overline{A}+\overline{B}\right)=\left(\overline{A}+B\right)\left(A+\overline{B}\right)=AB+\overline{A}\overline{B}$

<p>Using truth table of logic gates</p><p><math><mrow><mi>Y</mi><mo>=</mo><mover accent="true"><mrow><mrow><mo> (</mo><mrow><mi>A</mi><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo> (</mo><mrow><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mi>B</mi></mrow><mo>)</mo></mrow></mrow><mo stretchy="true">¯</mo></mover><mo>=</mo><mover accent="true"><mrow><mrow><mo> (</mo><mrow><mrow><mo> (</mo><mrow><mi>A</mi><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo stretchy="true">¯</mo></mover><mover accent="true"><mrow><mrow><mo> (</mo><mrow><mrow><mo> (</mo><mrow><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mi>B</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo stretchy="true">¯</mo></mover></mrow></math></p><p><math><mrow><mi>Y</mi><mo>=</mo><mrow><mo> (</mo><mrow><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mo>+</mo><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow><mo>)</mo></mrow><mrow><mo> (</mo><mrow><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mo>+</mo><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo> (</mo><mrow><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mo>+</mo><mi>B</mi></mrow><mo>)</mo></mrow><mrow><mo> (</mo><mrow><mi>A</mi><mo>+</mo><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow><mo>)</mo></mrow><mo>=</mo><mi>A</mi><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow></math></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755055612phprvsk1s.jpeg" alt="" width="355" height="114" loading="lazy"></picture></div></div>

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