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: 5 minutes
Maharashtra State Board: Class 12
Key Points: Algebra of Statements
| Law | Statement(s) |
|---|---|
| Idempotent Law | \[\begin{array} {l}p\lor p\equiv p \\ p\land p\equiv p \end{array}\] |
| Commutative Law | \[\begin{aligned} & p\lor q\equiv q\lor p \\ & p\land q\equiv q\land p \end{aligned}\] |
| Associative Law | \[(p\lor q)\lor r\equiv p\lor(q\lor r)\equiv p\lor q\lor r\] \[(p\land q)\land r\equiv p\land(q\land r)\equiv p\land q\land r\] |
| Distributive Law | \[p\lor(q\land r)\equiv(p\lor q)\land(p\lor r)\] \[p\land(q\lor r)\equiv(p\land q)\lor(p\land r)\] |
| Identity Law | \[p\lor F\equiv p\] \[p\wedge T\equiv p\] \[p\lor T\equiv T\] \[p\wedge F\equiv F\] |
| Complement Law | \[\begin{array} {l}p\lor\sim p\equiv T \\ p\land\sim p\equiv F \end{array}\] |
| Absorption Law | \[\begin{array} {l}p\lor(p\land q)\equiv p \\ p\land(p\lor q)\equiv p \end{array}\] |
| De Morgan’s Law | \[\sim(p\lor q)\equiv\sim p\land\sim q\] \[\sim(p\wedge q)\equiv\sim p\vee\sim q\] |
| Conditional Law | \[p\to q\equiv\sim p\lor q\] |
| Biconditional Law | \[p\leftrightarrow q\equiv(p\to q)\land(q\to p)\]\[\equiv(\sim p\lor q)\land(\sim q\lor p)\] |
