What does this mean? Whats the difference between IFF and IF?

  • Context: High School 
  • Thread starter Thread starter BloodyFrozen
  • Start date Start date
  • Tags Tags
    Difference Mean
Click For Summary
SUMMARY

The discussion clarifies the distinction between "IFF" (if and only if) and "IF" in logical expressions. "IF" is represented as A -> B, indicating that if A is true, then B is also true. In contrast, "IFF" is denoted as A <-> B, meaning both A and B must share the same truth value—either both are true or both are false. To prove an IFF statement, one must demonstrate both A -> B and B -> A, often requiring separate proofs for each direction.

PREREQUISITES
  • Understanding of basic logical operators, including implication and equivalence.
  • Familiarity with logical notation such as A -> B and A <-> B.
  • Knowledge of truth values and how they apply to logical statements.
  • Experience with constructing logical proofs, particularly in mathematical contexts.
NEXT STEPS
  • Study logical equivalences in propositional logic.
  • Learn about truth tables and their application in evaluating logical statements.
  • Explore proof techniques, focusing on direct proofs and proof by contradiction.
  • Investigate the role of logical implications in mathematical reasoning and proofs.
USEFUL FOR

This discussion is beneficial for students of mathematics, computer science professionals, and anyone interested in improving their understanding of logical reasoning and proof construction.

BloodyFrozen
Messages
353
Reaction score
1
What does this mean? Whats the difference between IFF and IF?
 
Mathematics news on Phys.org


BloodyFrozen said:
What does this mean? Whats the difference between IFF and IF?
Logical implication A -> B can be expressed as if A then B.

A -> B and B -> A can be expressed as iff A then B.
 


mathman said:
Logical implication A -> B can be expressed as if A then B.

A -> B and B -> A can be expressed as iff A then B.

Oh, I see now.

A<->B is iff

and A->B is if
 


BloodyFrozen said:
Oh, I see now.

A<->B is iff

and A->B is if

Another way to think about it is that A \Leftrightarrow B means that A and B have the same truth value. Either both are true or both are false.

If you are asked to do a proof of an IFF statement, you should break it down into two proofs: one of A \Rightarrow B and the other of B \Rightarrow A. Typically one direction will be easier than the other.
 

Similar threads

High School What does 2:3 ratio mean? What does it show?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Connection between mean and median
  • · Replies 3 ·
Replies
3
Views
1K
High School The difference between the symbols ##=## and ##\equiv##
  • · Replies 6 ·
Replies
6
Views
1K
MHB What does the following means?
  • · Replies 2 ·
Replies
2
Views
1K
High School What does it mean to "do mathematics"?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad What does f(t) Subscripted to g(t) Epsilon Mean?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Solve Brainteaser: What's the Difference in Age Between Steve and Steveston?
  • · Replies 20 ·
Replies
20
Views
2K
High School Arithmetic mean of an infinite number of points?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad What is the difference between a well-defined relation and a function?
  • · Replies 2 ·
Replies
2
Views
2K
High School What Does It Mean If an Expression Is Equal to Another Expression?
  • · Replies 22 ·
Replies
22
Views
3K