PROPOSITIONS ○ Conditional →
Logic - Also known as implication
- The study of arguments - Conditional statement (Read as
- The discipline that considers the “If P, then Q”)
methods of reasoning - Remember: the rule of the second
- It’s objective is to identify the correct statement MUST be followed; it is
and incorrect arguments true when both P and Q are true
Prepositions or when P is false, it is false when
- Also known as statements P is true and Q is false, but true
- A declarative statement that is when both are false
either true or false but not both. ○ Biconditional ↔
- In contrast, a non-statement is - Biconditional Statement (Read as
neither true nor false “P if and only if Q” or “P is
Propositional Variables equivalent to Q”)
- Arbitrary proposition with unspecified - Remember: if it’s not equal, then
truth value it is false
- Denoted by a capital letter of the ❖ Converse
English alphabet - Q→P
- Example: let E represent “3 is an - Reverse
even number.” ❖ Inverse
❖ Simple Proposition - ~P → ~Q
- Does not contain any other - Negation
statement as a component part ❖ Contrapositive
❖ Compound Proposition - ~Q → ~P
- Contains another proposition as a - Reverse and negation
component part
- Proposition inside another TRUTH TABLES
proposition Equivalent Statements
Propositional Forms - Two statement with the same truth
- Sequences of symbols value
● Sentence Letters - Have identical truth values in their
● Logical Operators final columns
○ And ∧ - P≡Q
- Conjunction of P and Q (Read as Tautology
“P and Q”) - Always true
- Remember: a false in AND will Contradiction
result to false - Always false
○ Or ∨ Contingency
- Disjunction of P and Q (Read as - Neither tautology nor contradiction
“P or Q”)
- Remember: a true in OR will
result to true
○ Not ~ / ¬ / -
- Negation of P (Read as “not P”)
Logic - Also known as implication
- The study of arguments - Conditional statement (Read as
- The discipline that considers the “If P, then Q”)
methods of reasoning - Remember: the rule of the second
- It’s objective is to identify the correct statement MUST be followed; it is
and incorrect arguments true when both P and Q are true
Prepositions or when P is false, it is false when
- Also known as statements P is true and Q is false, but true
- A declarative statement that is when both are false
either true or false but not both. ○ Biconditional ↔
- In contrast, a non-statement is - Biconditional Statement (Read as
neither true nor false “P if and only if Q” or “P is
Propositional Variables equivalent to Q”)
- Arbitrary proposition with unspecified - Remember: if it’s not equal, then
truth value it is false
- Denoted by a capital letter of the ❖ Converse
English alphabet - Q→P
- Example: let E represent “3 is an - Reverse
even number.” ❖ Inverse
❖ Simple Proposition - ~P → ~Q
- Does not contain any other - Negation
statement as a component part ❖ Contrapositive
❖ Compound Proposition - ~Q → ~P
- Contains another proposition as a - Reverse and negation
component part
- Proposition inside another TRUTH TABLES
proposition Equivalent Statements
Propositional Forms - Two statement with the same truth
- Sequences of symbols value
● Sentence Letters - Have identical truth values in their
● Logical Operators final columns
○ And ∧ - P≡Q
- Conjunction of P and Q (Read as Tautology
“P and Q”) - Always true
- Remember: a false in AND will Contradiction
result to false - Always false
○ Or ∨ Contingency
- Disjunction of P and Q (Read as - Neither tautology nor contradiction
“P or Q”)
- Remember: a true in OR will
result to true
○ Not ~ / ¬ / -
- Negation of P (Read as “not P”)
