solution on which

USAGE SUMMARY

The phrase "solution on which" is correct and usable in written English.
It can be used when referring to a specific solution that is the basis for further discussion or analysis. Example: "We need to focus on the solution on which our project depends to ensure its success."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

And when such leadership is in power, a peace agreement — and the two-state solution on which it can only be based — is anything but an illusion.

The New York Times

If such a weakening seems to amount to epiphenomenalism, you might look for an inheritance solution on which mental properties are efficacious in the same sense that their physical realizers are (compare the "homogeneity assumption" in Crane 1995).

SEP

It was found that the use of artificial intelligence in the outsourcing function of SRM to identify appropriate suppliers to form a supply network has become a promising solution on which manufacturers depend for products, services and distribution.

Expert Systems with Applications

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

These extremists make sensible, reasonable gun control hard to discuss, let alone achieve in this country, because they skew the conversations away from common-sense solutions on which both rational gun owners and non-gun owners can agree.

The New York Times

Suppose that the reduced equation has two isolated solutions on, which satisfy the following condition: (12).

Boundary Value Problems

In this section, the relevant background is provided to power flow analysis and dynamic programming, and the approximations to their solutions on which the distributed problem and solution of the paper are built.

Journal of Modern Power Systems and Clean Energy

That is, in cases where there are no clear evidenced-based solutions on which course of treatment should be adopted, health care teams help people to work through their values and preferences (O'Connor et al. 2004, 63 ).

American Journal of Bioethics

"You will be dealing with big tasks on the solution of which our country's future will depend," he said.

Unicef

However, it is known that the solution depends on which method factor is excluded from the model as the reference.

Large-scale Assessments in Education

To this end, [8] considers RD optimal WZ quantization (RD-WZQ) model, the solution based on which is appropriate for practical block quantization techniques such as TCQ.

EURASIP Journal on Advances in Signal Processing

For some special cases, we derive a number of properties of the optimal solution, based on which we design heuristics and branch-and-bound algorithms to solve these problems.

Computers & Operations Research

Expert writing Tips

Best practice

Use "solution on which" to clearly indicate that a particular solution serves as the groundwork or prerequisite for subsequent actions, discussions, or analyses. For example: "The peace agreement is the solution on which all future negotiations will be based."

Common error

Avoid using "solution on which" when the connection between the solution and the subsequent element is weak or unclear. Be precise about how the solution directly enables or influences what follows. For example, instead of saying "a solution on which progress can be made," specify what aspect of the solution facilitates progress.

Linguistic Context

The phrase "solution on which" functions as a prepositional phrase indicating that the "solution" serves as the foundation, basis, or prerequisite for something else. As Ludwig AI confirms, it's a valid English construction. Examples provided demonstrate its use in various contexts, primarily to specify dependency.

Expression frequency: Rare

Frequent in

Science

60%

News & Media

20%

Formal & Business

20%

Less common in

Ludwig's WRAP-UP

In summary, "solution on which" is a grammatically correct phrase used to emphasize that a specific solution is the basis or foundation for something else. Ludwig AI confirms its validity, and while the phrase is somewhat rare, it's primarily found in scientific, news, and formal business contexts. To ensure clarity, use it to precisely specify how a solution directly enables or influences subsequent actions. Remember that alternatives like "basis upon which" or "foundation upon which" can be used to add variety while maintaining semantic equivalence.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

basis upon which

Replaces "solution" with "basis", emphasizing the foundation for something else.

foundation upon which

Substitutes "solution" with "foundation", highlighting a structural support.

grounds on which

Changes "solution" to "grounds", focusing on reasons or justifications.

principle on which

Replaces "solution" with "principle", emphasizing a guiding belief or rule.

premise on which

Substitutes "solution" with "premise", highlighting an assumption.

framework on which

Changes "solution" to "framework", focusing on a structural plan.

platform on which

Replaces "solution" with "platform", highlighting a base for building.

approach that relies on

Alters the structure to emphasize reliance on a specific approach.

method that depends on

Changes the structure to focus on dependency on a specific method.

strategy centered around

Shifts the focus to a strategy with the center around something else.

FAQs

How can I use "solution on which" in a sentence?

Use "solution on which" to indicate that a specific solution acts as a foundation or basis for further actions or considerations. For example: "The agreed-upon framework is the "solution on which" we will build our future strategies."

What are some alternatives to "solution on which"?

Alternatives include "basis upon which", "foundation upon which", or "grounds on which", depending on the specific nuance you want to convey. Each alternative emphasizes a slightly different aspect of the foundational relationship.

Is "solution on which" formal or informal?

"Solution on which" is generally considered a formal phrase, suitable for academic, professional, or news-related contexts. In more informal settings, simpler alternatives may be preferred.

What's the difference between "solution on which" and "solution that"?

"Solution on which" explicitly indicates a dependent relationship, where something relies on the solution. "Solution that" is a more general construction, simply describing a characteristic of the solution without necessarily implying dependency.