Question:
If $\mathrm{q}$ is false and $\mathrm{p} \wedge \mathrm{q} \leftrightarrow \mathrm{r}$ is true, then which one of the following statements is a tautology?
$(\mathrm{p} \vee \mathrm{r}) \rightarrow(\mathrm{p} \wedge \mathrm{r})$
$p \vee r$
$p \wedge r$
$(p \wedge r) \rightarrow(p \vee r)$
Correct Option: , 4
Solution:
Given $q$ is $F$ and $(p \wedge q) \leftrightarrow r$ is $T$
$\Rightarrow \mathrm{p} \wedge \mathrm{q}$ is $\mathrm{F}$ which implies that $\mathrm{r}$ is $\mathrm{F}$
$\Rightarrow \mathrm{q}$ is $\mathrm{F}$ and $\mathrm{r}$ is $\mathrm{F}$
$\Rightarrow(\mathrm{p} \wedge \mathrm{r})$ is always $F$
$\Rightarrow(\mathrm{p} \wedge \mathrm{r}) \rightarrow(\mathrm{p} \vee \mathrm{r})$ is tautology.
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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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