Question 19

The correct truth table for the following logic circuit is :

Name: The correct truth table for the following logic circuit is :
Uploaded: 2026-05-20T11:08:36.269015+05:30
Duration: 1 min 52 s
Description: The correct truth table for the following logic circuit is :

Solution

$$\text{Top input} = \bar{A} \quad (\text{via NOT gate})$$

$$\text{Bottom input} = A \cdot B \quad (\text{via AND gate})$$

$$Y = \bar{A} + (A \cdot B)$$

Using the distributive law of Boolean algebra ($$X + (\bar{X} \cdot Y) = X + Y$$):

$$Y = (\bar{A} + A) \cdot (\bar{A} + B)$$

$$\implies Y = 1 \cdot (\bar{A} + B) = \bar{A} + B$$

For $$A=0, B=0 \implies Y = \bar{0} + 0 = 1 + 0 = 1$$

For $$A=0, B=1 \implies Y = \bar{0} + 1 = 1 + 1 = 1$$

For $$A=1, B=0 \implies Y = \bar{1} + 0 = 0 + 0 = 0$$

For $$A=1, B=1 \implies Y = \bar{1} + 1 = 0 + 1 = 1$$

Get AI Help

Video Solution

Create a FREE account and get:

Free JEE Mains Previous Papers PDF
Take JEE Mains paper tests

JEE Quant Questions | JEE Quantitative Ability

JEE DILR Questions | LRDI Questions For JEE

JEE Verbal Ability Questions | VARC Questions For JEE

Free JEE Topicwise Questions

JEE Rotational Motion JEE Units & Measurements JEE Atomic Structure JEE Gravitation JEE Periodic Table & Periodicity JEE Statistics JEE Inverse Trigonometric Functions JEE Magnetism & Magnetic Materials JEE Sequences & Series JEE Matrices JEE Alternating Currents JEE Carboxylic Acids JEE Permutations & Combinations JEE Work, Energy & Power JEE Electromagnetic Induction JEE Electronic Devices JEE d and f-Block Elements JEE Chemical Kinetics JEE Heat Transfer JEE Three Dimensional Geometry JEE Magnetic Effects of Current JEE Hydrocarbons - Aromatic JEE Electromagnetic Waves JEE Aldehydes & Ketones JEE Hydrocarbons - Alkanes JEE Applications of Derivatives JEE Equilibrium JEE Indefinite Integration JEE Chemical Thermodynamics JEE Electrochemistry JEE Probability JEE Biomolecules JEE Continuity & Differentiability JEE Kinetic Theory of Gases JEE Vector Algebra JEE Hydrocarbons - Alkynes JEE Differential Equations JEE Current & Resistance JEE Straight Lines JEE Waves JEE Redox Reactions JEE Hydrocarbons - Alkenes JEE Determinants JEE Solutions JEE Ray Optics JEE Dual Nature of Matter & Radiation JEE Chemical Bonding & Molecular Structure JEE Complex Numbers JEE Sets, Relations & Functions JEE Electric Charges & Fields JEE Laws of Motion JEE Fluid Mechanics JEE Basic Concepts in Chemistry JEE Trigonometric Functions JEE Limits JEE Laws of Thermodynamics JEE Kinematics - 2D Motion JEE p-Block Elements (Groups 13-18)JEE Simple Harmonic Motion JEE Electric Potential & Capacitance JEE Coordination Compounds JEE JEE 2D Geometry JEE Circles JEE Definite Integration JEE EMF & Circuit Analysis JEE Surface Tension JEE Atoms & Nuclei JEE Laboratory Experiments - XI JEE Number System JEE Basic Principles of Organic Chemistry JEE Wave Optics JEE Quadratic Equations JEE Alcohols, Phenols & Ethers JEE Organic Compounds with Halogens JEE Differentiation JEE Conic Sections JEE Nitrogen-Containing Compounds JEE Elasticity JEE Practical Organic Chemistry JEE Kinematics - 1D Motion JEE Purification & Characterisation JEE Binomial Theorem