If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:
(i) $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
(ii) $(A \cap B)^{\prime}=A^{\prime} B^{\prime}$.
Given:
U = {2, 3, 5, 7, 9}
A = {3, 7}
B = {2, 5, 7, 9}
To prove :
(i) $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
(ii) $(A \cap B)^{\prime}=A^{\prime} \cup B$,
Proof :
(i) LHS:
$(A \cup B)=\{2,3,5,7,9\}$
$(A \cup B)^{\prime}=\phi$
RHS
$A^{\prime}=\{2,5,9\}$
$B^{\prime}=\{3\}$
$A^{\prime} \cap B^{\prime}=\phi$
LHS = RHS
$\therefore(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
(ii) LHS
$(A \cap B)=\{7\}$
$(A \cap B)^{\prime}=\{2,3,5,9\}$
RHS
$A^{\prime}=\{2,5,9\}$
$B^{\prime}=\{3\}$
$A^{\prime} \cup B^{\prime}=\{2,3,5,9\}$
LHS = RHS
$\therefore(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,