Section 1

CFA Level 1 - Cheatsheet

STUDY GUIDE

🎓 CFA Level 1 - Study Guide

📋 Course Structure


code
📚 CFA Level 1
├── 📖 Chapter 1: Propositional Logic
│   ├── 🔹 Propositions and Logical Operators
│   ├── 🔹 Precedence Rules and Compound Propositions
│   ├── 🔹 Logical Equivalence and Truth Tables
│   └── 🔹 Other Logical Operators
├── 📖 Chapter 2: Boolean Algebra
│   ├── 🔹 Laws of Boolean Algebra
│   ├── 🔹 Simplifications and Substitution Laws
│   └── 🔹 Functional Completeness
├── 📖 Chapter 3: Logic Circuits
│   ├── 🔹 Logic Gates
│   ├── 🔹 Combining Gates and Combinatorial Logic Circuits
│   └── 🔹 Disjunctive Normal Form (DNF)
├── 📖 Chapter 4: Predicate Logic
│   ├── 🔹 Predicates and Domains of Discourse
│   ├── 🔹 Quantifiers
│   └── 🔹 DeMorgan's Laws for Predicate Logic
├── 📖 Chapter 5: Deduction
│   ├── 🔹 Valid Arguments and Rules of Inference
│   └── 🔹 Formal Proofs and Counterexamples
└── 📖 Chapter 6: Ethical and Professional Standards in Investment Management
    ├── 🔹 Conflicts of Interest
    ├── 🔹 Material Nonpublic Information
    ├── 🔹 Fair Dealing and Priority of Transactions
    └── 🔹 Responsibilities of Supervisors and Compliance

Section 2

📖 Chapter 1: Propositional Logic

What this chapter covers: This chapter introduces the basic building blocks of logic: propositions and logical operators. It explains how to combine propositions to form compound statements, the rules that govern the order of operations, and how to determine if two statements are logically equivalent using truth tables. The chapter also covers additional logical operators beyond the basic AND, OR, and NOT.

🔑 Essential Concepts & Formulas

Concept/Formula	Definition/Equation	When to Use	Quick Check
Proposition	A statement that is either true or false.	Identifying valid logical arguments.	Check if the statement can be assigned a truth value.
Conjunction (AND)	$p \land q$	When both p and q must be true.	Check if both propositions are true in the given scenario.
Disjunction (OR)	$p \lor q$	When at least one of p or q must be true.	Check if at least one proposition is true in the given scenario.
Negation (NOT)	$\neg p$	When the opposite of p is required.	Check if the proposition is false in the given scenario.
Conditional (Implication)	$p \to q$	To express "if p, then q".	Verify that $p$ being true implies $q$ is also true.
Biconditional (Equivalence)	$p \leftrightarrow q$	To express "p if and only if q".	Verify that $p$ and $q$ have the same truth value.

🛠️ Problem Types

Type A: Evaluating Compound Propositions

Setup: "Given the truth values of individual propositions, determine the truth value of a complex logical statement involving multiple operators."

Method: "Apply precedence rules (NOT, AND, OR) and truth tables for each operator to systematically evaluate the expression."

Final Answer

Example: "If

p

is true,

q

is false, and

r

is true, what is the truth value of

(p \land q) \lor \neg r

?" Solution:

(T \land F) \lor \neg T = F \lor F = F

Type B: Determining Logical Equivalence

Setup: "Determine whether two logical expressions are equivalent by constructing truth tables for both and comparing the results."

Method: "Create truth tables for each expression, listing all possible combinations of truth values for the variables. If the final columns of the truth tables are identical, the expressions are equivalent."

Example: "Are $p \to q$ and $\neg p \lor q$ logically equivalent? Construct truth tables to verify."

🧮 Solved Example

Problem: Determine the truth value of the proposition $(p \land q) \to (p \lor q)$ when $p$ is false and $q$ is true.

Given: $p = F$ , $q = T$

Steps:

Evaluate $p \land q$ : $F \land T = F$
Evaluate $p \lor q$ : $F \lor T = T$
Evaluate $(p \land q) \to (p \lor q)$ : $F \to T = T$

"

✅
Answer: The truth value is True.

⚠️ Common Mistakes

❌ Mistake 1: Incorrectly applying precedence rules.

✅ How to avoid: Always remember the order: NOT, AND, OR. Use parentheses for clarity.

❌ Mistake 2: Confusing conditional and biconditional operators.

✅ How to avoid: Remember that $p \to q$ is only false when $p$ is true and $q$ is false, while $p \leftrightarrow q$ is true only when $p$ and $q$ have the same truth value.

💡 Study Tip

Practice constructing truth tables for various logical expressions. This will help you understand the behavior of different operators and identify logical equivalences.

📖 Chapter 2: Boolean Algebra

What this chapter covers: This chapter introduces the rules and laws of Boolean algebra, which are used to simplify and manipulate logical expressions. It covers important laws such as DeMorgan's laws, distributive laws, and identity laws. The chapter also discusses the concept of functional completeness, which relates to the minimum set of operators needed to express any logical function.

🔑 Essential Concepts & Formulas

Concept/Formula	Definition/Equation	When to Use	Quick Check
Double Negation	$\neg(\neg p) = p$	Simplifying expressions with nested negations.	Verify by constructing a truth table.
DeMorgan's Law	$\neg(p \land q) = \neg p \lor \neg q$ $\neg(p \lor q) = \neg p \land \neg q$	Simplifying negated compound propositions.	Verify by constructing a truth table.
Distributive Law	$p \land (q \lor r) = (p \land q) \lor (p \land r)$ $p \lor (q \land r) = (p \lor q) \land (p \lor r)$	Expanding or factoring logical expressions.	Verify by constructing a truth table.
Identity Law	$p \land T = p$ $p \lor F = p$	Simplifying expressions involving true or false.	Substitute values to confirm.
Excluded Middle	$p \lor \neg p = T$	Proving tautologies.	Always true, regardless of $p$ .
Contradiction	$p \land \neg p = F$	Proving contradictions.	Always false, regardless of $p$ .

🛠️ Problem Types

Type A: Simplifying Boolean Expressions

Setup: "Given a complex Boolean expression, use the laws of Boolean algebra to reduce it to its simplest form."

Method: "Apply DeMorgan's laws, distributive laws, identity laws, and other Boolean algebra rules to systematically simplify the expression."

Final Answer

Example: "Simplify the expression

\neg (p \land \neg q) \lor q

." Solution:

\neg (p \land \neg q) \lor q = (\neg p \lor \neg (\neg q)) \lor q = (\neg p \lor q) \lor q = \neg p \lor (q \lor q) = \neg p \lor q

Type B: Proving Logical Equivalences using Boolean Algebra

Setup: "Prove that two logical expressions are equivalent by transforming one expression into the other using Boolean algebra laws."

Method: "Start with one expression and apply Boolean algebra laws step-by-step until it is identical to the other expression."

Final Answer

Example: "Prove that

p \to q

is equivalent to

\neg p \lor q

using Boolean algebra." Solution:

p \to q = \neg p \lor q

🧮 Solved Example

Problem: Simplify the Boolean expression $(p \land q) \lor (p \land \neg q)$ .

Given: Expression: $(p \land q) \lor (p \land \neg q)$

Steps:

Apply the distributive law: $p \land (q \lor \neg q)$
Apply the excluded middle law: $p \land T$
Apply the identity law: $p$

"

✅
Answer: $p$

⚠️ Common Mistakes

❌ Mistake 1: Incorrectly applying DeMorgan's laws.

✅ How to avoid: Remember to negate both propositions and change the operator (AND to OR, OR to AND).

❌ Mistake 2: Forgetting to apply the distributive law correctly.

✅ How to avoid: Ensure that you distribute the term to both propositions inside the parentheses.

💡 Study Tip

Practice simplifying various Boolean expressions. This will help you become familiar with the different laws and how to apply them effectively.

📖 Chapter 3: Logic Circuits

What this chapter covers: This chapter bridges the gap between propositional logic and digital electronics by introducing logic gates, which are the fundamental building blocks of logic circuits. It explains how these gates (AND, OR, NOT) implement logical operations and how they can be combined to create more complex circuits. The chapter also covers combinatorial logic circuits and the concept of disjunctive normal form (DNF).

🔑 Essential Concepts & Formulas

Concept/Formula	Definition/Equation	When to Use	Quick Check
AND Gate	Output is 1 only if all inputs are 1.	Implementing logical conjunction.	Verify output for all possible input combinations.
OR Gate	Output is 1 if at least one input is 1.	Implementing logical disjunction.	Verify output for all possible input combinations.
NOT Gate	Output is the inverse of the input.	Implementing logical negation.	Verify output for both possible input values.
Combinatorial Circuit	A circuit with no feedback loops.	Designing circuits for logical functions.	Ensure no output depends on a previous state.
Disjunctive Normal Form (DNF)	A disjunction of conjunctions.	Representing any truth table as a circuit.	Verify that the DNF expression matches the truth table.

🛠️ Problem Types

Type A: Designing Logic Circuits from Boolean Expressions

Setup: "Given a Boolean expression, design a logic circuit that implements the expression using AND, OR, and NOT gates."

Method: "Break down the expression into smaller parts and implement each part with the appropriate gate. Connect the gates according to the structure of the expression."

Example: "Design a logic circuit for the expression $(A \land B) \lor \neg C$ ."

Type B: Determining the Boolean Expression for a Logic Circuit

Setup: "Given a logic circuit, determine the Boolean expression that the circuit implements."

Method: "Trace the circuit from the inputs to the output, writing down the expression for each gate. Combine the expressions according to the connections in the circuit."

Final Answer

Example: "Determine the Boolean expression for a circuit with inputs A, B, and C, where A and B are inputs to an AND gate, and the output of the AND gate and C are inputs to an OR gate." Solution:

(A \land B) \lor C

🧮 Solved Example

Problem: Design a logic circuit for the Boolean expression $(A \lor B) \land \neg C$ .

Given: Expression: $(A \lor B) \land \neg C$

Steps:

Implement $A \lor B$ using an OR gate with inputs A and B.
Implement $\neg C$ using a NOT gate with input C.
Implement $(A \lor B) \land \neg C$ using an AND gate with the outputs of the OR and NOT gates as inputs.

"

✅
Answer: A circuit with an OR gate for A and B, a NOT gate for C, and an AND gate combining the outputs.

⚠️ Common Mistakes

❌ Mistake 1: Incorrectly connecting logic gates.

✅ How to avoid: Carefully trace the connections and ensure they match the Boolean expression.

❌ Mistake 2: Misunderstanding the behavior of logic gates.

✅ How to avoid: Review the truth tables for AND, OR, and NOT gates.

💡 Study Tip

Practice converting between Boolean expressions and logic circuits. This will help you understand the relationship between logic and hardware.

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CFA Level 1 - Cheatsheet

Study Notes Preview

CFA Level 1 - Cheatsheet

🎓 CFA Level 1 - Study Guide

📋 Course Structure

📖 Chapter 1: Propositional Logic

🔑 Essential Concepts & Formulas

🛠️ Problem Types

🧮 Solved Example

⚠️ Common Mistakes

💡 Study Tip

📖 Chapter 2: Boolean Algebra

🔑 Essential Concepts & Formulas

🛠️ Problem Types

🧮 Solved Example

⚠️ Common Mistakes

💡 Study Tip

📖 Chapter 3: Logic Circuits

🔑 Essential Concepts & Formulas

🛠️ Problem Types

🧮 Solved Example

⚠️ Common Mistakes

💡 Study Tip

5 more sections