if and only if

USAGE SUMMARY

"if and only if" is a correct and usable expression in written English.
You should use it when you want to conditionally connect two events or ideas. For example, "You can join the club if and only if you pay the membership fee."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

if and only if.

Journal of Inequalities and Applications

(b) if and only if.

Fixed Point Theory and Applications

or if and only if.

Journal of Inequalities and Applications

(vi) if and only if.

Journal of Inequalities and Applications

(i) if and only if.

Fixed Point Theory and Applications

Obviously, if and only if,.

Advances in Difference Equations

if and only if (224).

Journal of Inequalities and Applications

(ii) if and only if.

Fixed Point Theory and Applications

if and only if either.

Journal of Inequalities and Applications

So, if and only if.

Boundary Value Problems

Clearly, if and only if.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

Use "if and only if" to establish a clear, bidirectional relationship between two statements, ensuring that one is true precisely when the other is.

Common error

Avoid using "if and only if" when you only mean "if". "If" indicates a sufficient condition, whereas "if and only if" indicates a condition that is both necessary and sufficient.

Linguistic Context

The phrase "if and only if" functions as a logical connective, establishing a biconditional relationship between two statements. According to Ludwig, this phrase is correctly used to indicate that one statement is true precisely when the other is, creating a two-way implication.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, the phrase "if and only if" is a logical connective used to establish a biconditional relationship between two statements. Ludwig AI confirms its correct usage in written English, particularly in formal and scientific contexts, such as the Journal of Inequalities and Applications. It's crucial to differentiate "if and only if" from "if", as the former denotes a necessary and sufficient condition, while the latter indicates only a sufficient condition. Alternatives include "is equivalent to" and "when and only when", but the choice depends on the specific context and desired level of formality. Common errors involve misusing "if and only if" when a simple "if" suffices.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

when and only when

Adds emphasis to the necessity of both the condition and its exclusivity.

if, but only if

Provides a more direct and slightly less formal alternative, emphasizing the single, exclusive condition.

is a necessary and sufficient condition for

States the dual requirement of necessity and sufficiency for a condition to hold.

is equivalent to

Focuses on the equivalence between two statements or conditions, highlighting their interchangeable nature.

implies and is implied by

Highlights the bidirectional implication between two statements, focusing on logical consequence.

precisely when

Emphasizes the exact moment or condition under which something occurs, providing a sense of exactness and timing.

is defined as

Highlights that two concepts are logically equivalent because one is defined in terms of the other

necessitates and is necessitated by

Emphasizes mutual dependence, indicating that each condition is both required for and results from the other.

exactly under the circumstance that

Underscores the precise scenario or situation in which something is true or valid.

just in case that

Highlights that something only happens under a particular condition.

FAQs

What is the meaning of "if and only if"?

The phrase "if and only if" indicates that one statement is true exactly when another statement is true. It establishes a bidirectional logical relationship, meaning the first statement implies the second, and the second implies the first.

How do I use "if and only if" in a sentence?

Use "if and only if" to connect two statements where the truth of one depends entirely on the truth of the other. For example, "A triangle is equilateral if and only if all its sides are equal."

What can I say instead of "if and only if"?

You can use alternatives like "is equivalent to", "when and only when", or "is a necessary and sufficient condition for" depending on the context.

Is there a shorter way to write "if and only if"?

In mathematical and logical contexts, "if and only if" is often abbreviated as "iff". While concise, this abbreviation is generally not appropriate for all forms of writing and should be used with discretion.