Englishfor English speakers
assumption
Noun
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An assumption is a guess or belief about something without having enough information to know if it is true. In maths or science: something assumed to be true in order to build an argument or calculation.
You shouldn't make the assumption that guns are only a problem in big cities.
To calculate the age of a rock we make the assumption that the rate of radioactive decay is constant.
clause
Noun
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A clause is a section in a contract or other legal document.
The author's contract contained a clause giving him creative control over the films.
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A clause is a group of words that usually includes a subject and a predicate. In English, the subject usually comes before the predicate.
The last clause in the sentence is hard to understand without knowing some background.