You only use definite articles with specified things, for example, in 'enjoying the sun' we are not referring to the star itself but the light, mood and warmth emitted by it. However, in 'plants need sun' we are referring to the star itself therefore it is considered as a whole concrete noun, so we use 'the' when referring to it.
All day is a fixed expression that means the same thing as the whole day. Your grammar book is correct.
All of the day is grammatical but not idiomatic in the sense of being an established expression. So your example sentence is fine. More often, people might say We spent all of that day on the beach, referring back to an occasion that they have already ...
Because you have "that" acting as a determiner, you don't need an article as well.
after that first year.
Consider as an example:
Look at the car.
Look at that car.
Both "the" and "that" in these two examples serve to highlight which particular car you mean.
When you use:
For the efficient running of the business...
then "running" behaves more like a noun, being paired with an adjective ("efficient") and followed by a genitive ("of the business"). That is the main reason why the omitting of the definite article is not grammatically correct.
The definite article is needed in order ...
Your textbook is correct. Yes, we really do need the definite article there. It announces an approaching gerund: running.
Although you're right in thinking "the house" is specific and "a house" is not, there is nothing specific about the efficient running. In "the stealing of other people's property is illegal" there is no ...
When we think of meal as a process, not as an event, we use no article.
How was the dinner?
In this case, "the dinner" often refers to the meal as an event.
How was dinner?
In this case, "dinner" simply refers to an evening meal.
So if there's a special event use "the" otherwise simply use:
How was dinner last night?...
We usually talk about the bill for something. Otherwise, your interpretations are correct. We would use the definite article ('the') for the only bill, and the indefinite article ('a') for a bill which is, or could be, one of a number.
#1 means that all members of the group (we) have US citizenship. It would be true of any group of US citizens.
#2 strictly means that the group includes every US citizen, and no others. It can really only be used by somebody who is speaking for the nation as a whole.
"An invention should be described in its dynamic state. The dynamic state is understood as a state in which... "
"An invention should be described in its dynamic state. A dynamic state is understood as the state in which... "
In this case, the articles can be used interchangeably.
"Taking delivery of" is an idiomatic compound verb meaning to receive something being delivered.
Placing "the" in front of "delivery" treats it as a noun. Delivery can be a noun in some contexts, but not this one. For example, we might say "He took the delivery to the back room." That would be used if we did not know ...