CS 225: Discrete Structures
FALL SEMESTER 2025
Module 1
In this module, you will explore Logical Form and Logical Equivalence & Conditional
Statements:
Here are important concepts to consider :
● Order of Operations in Logic: 1.Negation(~) 2. Conjunction, Disjunction; if applicable,
Parentheses will clarify the order (∧, ∨) 3. If, If and Only If (→,↔)
● Logical Laws: Commutative Laws, Associative Laws, Distributive Laws, Identity Laws,
Negation Laws, Double Negation, Idempotent Laws, Universal Bound Laws, De
Morgan’s Laws, Absorption Laws, Negations of Tautology and Contradiction
● Truth Tables: there are predetermined outcomes in both compound and conditional
statements, based on the relationships expressed.
Key Terms
Proposition: A definitive truth statement that can be classified as either “True” or “False,”
and is free of any ambiguity. Propositions can be combined to form compound statements.
Conjunction: the logical connective ‘and’ (for example: p∧q)
Disjunction: the logical connective ‘or’ (for example: p∨q)
Negation: the logical connective ‘not’ (for example: ~p)
Conditional Statements: An “if then, then the following” form of prediction in math and
logic. For example: u → v
Converse Statements: A conditional statement that is true in both directions.
1
FALL SEMESTER 2025
Module 1
In this module, you will explore Logical Form and Logical Equivalence & Conditional
Statements:
Here are important concepts to consider :
● Order of Operations in Logic: 1.Negation(~) 2. Conjunction, Disjunction; if applicable,
Parentheses will clarify the order (∧, ∨) 3. If, If and Only If (→,↔)
● Logical Laws: Commutative Laws, Associative Laws, Distributive Laws, Identity Laws,
Negation Laws, Double Negation, Idempotent Laws, Universal Bound Laws, De
Morgan’s Laws, Absorption Laws, Negations of Tautology and Contradiction
● Truth Tables: there are predetermined outcomes in both compound and conditional
statements, based on the relationships expressed.
Key Terms
Proposition: A definitive truth statement that can be classified as either “True” or “False,”
and is free of any ambiguity. Propositions can be combined to form compound statements.
Conjunction: the logical connective ‘and’ (for example: p∧q)
Disjunction: the logical connective ‘or’ (for example: p∨q)
Negation: the logical connective ‘not’ (for example: ~p)
Conditional Statements: An “if then, then the following” form of prediction in math and
logic. For example: u → v
Converse Statements: A conditional statement that is true in both directions.
1
