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The process is ended if the ‘a’ and ‘b’ values of the object are lower than the given value.
The process is ended if the condition ‘c’ is not fulfilled.

Can I combine these sentences as below?

The process is ended, if the ‘a’ and ‘b’ values of the object are lower than the given value or if the condition ‘c’ is not fulfilled.

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I would rather rephrase it as follows:

The process is ended if the object's values for a and b are lower than the given value, or if condition c is not verified.

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What is the relationship between the 2 sentences? Can one trump the other?

For example, if 'a' and 'b' are low enough does 'c' not matter? Conversely, if 'c' is not fulfilled can that end the process?

Basically you have to consider which of these is correct:

The process is ended, if the ‘a’ and ‘b’ values of the object are lower than the given value or if the condition ‘c’ is not fulfilled.

OR

The process is ended, if the ‘a’ and ‘b’ values of the object are lower than the given value and if the condition ‘c’ is not fulfilled.

These are quite different yet each could be correct.

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    Based on the question's wording, this is definitely an OR condition. If both of the given statements are true, then each independently ends the process. Therefore the process ends if either is true; an OR condition, not an AND. – WendiKidd Apr 9 '13 at 23:17
  • I've had situations where one was gathering requirements and would get bitten by collecting these statements only to be clarified that it was an intended AND instead of an assumed OR. – JB King Apr 9 '13 at 23:25
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    Be careful with and and logic. The English word and sometimes acts a bit like logical or because and in English works on sets - not on prepositions. For example We are now boarding customers with first class and business class tickets means we are now boarding the union of the set of customers holding first class tickets and the set of customers with business class tickets (NOT we are boarding the set of customers holding both first class and business class tickets), i.e. they are boarding customers holding a first class ticket logical OR holding a business class one. – Matt Apr 10 '13 at 5:13

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