Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
Estimated time: 4 minutes
- Negation of conjunction
- Negation of disjunction
- Negation of implication
- Negation of biconditional
Maharashtra State Board: Class 12
Key Points: Negation
| Statement | Negation |
|---|---|
| \[\sim(\sim p)\] | ( p ) |
| \[\sim(p\wedge q)\] | \[\sim p\lor q\] |
| \[\sim(p\lor q)\] | \[\sim p\wedge\sim q\] |
| \[\sim(p\to q)\] | \[p\wedge\sim q\] |
| \[\sim(p\leftrightarrow q)\] | \[(p\wedge\sim q)\vee(\sim p\wedge q)\] |
| \[\sim(\forall x)\] | \[\exists x\] |
| \[\sim(\exists x)\] | \[\forall x\] |
| \[\sim(x<y)\] | \[x\geq y\] |
| \[\sim(x>y)\] | \[x\leq y\] |
