Question:
Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L–(M∪N) = (L–M)∩(L–N).
Solution:
According to the question,
L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}
To verify:
L – (M ∪ N) = (L – M) ∩ (L – N)
M = {3, 4, 5, 6}, N = {1, 3, 5} ⇒ M ∪ N = {1, 3, 4, 5, 6}
L = {1, 2, 3, 4} and M ∪ N = {1, 3, 4, 5, 6}
⇒ L – (M ∪ N) = {2}………………(i)
L = {1, 2, 3, 4} and M = {3, 4, 5, 6} ⇒ L – M = {1, 2}
L = {1, 2, 3, 4} and N = {1, 3, 5} ⇒ L – N = {2, 4}
L – M = {1, 2} and L – N = {2, 4}
⇒ (L – M) ∩ (L – N) = {2}………………(ii)
From equations (i) and (ii),
We have,
L – (M ∪ N) = (L – M) ∩ (L – N)
Hence verified
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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,
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