Другое : Сравнительные степени прилагательных и наречий (Comparison) Модальные глаголы (Modal Verbs) Цепочки ...
Сравнительные степени прилагательных и наречий (Comparison) Модальные глаголы (Modal Verbs) Цепочки ...
Can, Could, Be able to
Can and could are modal auxiliary verbs. Be able to
uses the verb "to be" as a main verb. It is not an auxiliary verb,
but we look at it here for convenience.
Can
Can is an auxiliary verb, a modal auxiliary verb. We
use "can" to:
talk about possibility and ability
make requests
ask for or give permission
Structure of Can
subject + can + main verb
The main verb is always the bare infinitive (infinitive without
"to").
subject
auxiliary verb
main verb
+
I
can
play
tennis.
-
He
cannot
play
tennis.
can't
?
Can
you
play
tennis?
Notice that:
Can is invariable. There is only one form of can.
The main verb is always the bare infinitive.
Use of Can
can: Possibility and Ability
We use can to talk about what is possible, what we are able or free
to do:
She can drive a car.
John can speak Spanish.
I cannot hear you. (I can't hear you.)
Can you hear me?
Normally, we use can for the present. But it is possible to use can
when we make present decisions about future ability.
Can you help me with my homework? (present)
Sorry. I'm busy today. But I can help you tomorrow.
(future)
can: Requests and Orders
We often use can in a question to ask somebody to do something. This
is not a real question - we do not really want to know if the person is able to
do something, we want them to do it! The use of can in this way is
informal (mainly between friends and family):
Can you make a cup of coffee, please.
Can you put the TV on.
Can you come here a minute.
Can you be
quiet!
can: Permission
We sometimes use can to ask or give permission for something:
Can I smoke in this room?
You can't smoke here, but you can smoke in
the garden.
(Note that we also use could, may, might for permission. The use of can
for permission is informal.)
Could
Could is an auxiliary verb, a modal auxiliary verb. We
use "could" to:
talk about past possibility or ability
make requests
Structure of Could
subject + could + main verb
The main verb is always the bare infinitive (infinitive without
"to").
subject
auxiliary verb
main verb
+
My grandmother
could
speak
Japanese.
-
She
could not
speak
Chinese.
couldn't
?
Could
your grandmother
speak
Japanese?
Notice that:
Could is invariable. There is only one form of could.
The main verb is always the bare infinitive.
Use of Could
could: Past Possibility or Ability
We use could to talk about what was possible in the past, what we
were able or free to do:
I could swim when I was 5 years old.
My grandmother could speak seven languages.
When we arrived home, we could not open the door. (...couldn't open the door.)
Could you understand what he was saying?
We use could (positive) and couldn't (negative) for general
ability in the past. But when we talk about one special occasion in the past,
we use be able (positive) and couldn't (negative). Look at these examples:
Past
General
Specific Occasion
+
My grandmother could speak Spanish.
A man fell into the river yesterday. The police were
able to save him.
-
My grandmother couldn't speak Spanish.
A man fell into the river yesterday. The police couldn't
save him.
could: Requests
We often use could in a question to ask somebody to do something. The
use of could in this way is fairly polite (formal):
Could you tell me where the bank is, please?
Could you send me a catalogue, please?
Be able to
Although we look at be able to here, it is not a modal verb.
It is simply the verb "to be" plus an adjective (able) followed by
the infinitive. We look at "be able to" here because we sometimes use
it instead of "can" and "could". We use
"be able to":
to talk about ability
Structure of Be able to
The structure of be able to is:
subject + be + able + infinitive
subject
be main verb
able adjective
infinitive
+
I
am
able
to drive.
-
She
is not
able
to drive.
isn't
?
Are
you
able
to drive?
Notice that be able to is possible in all tenses, for example:
I was able to drive...
I will be able to drive...
I have been able to drive...
Notice too that be able to has an infinitive form:
I would like to be able to speak Chinese.
Use of Be able to
be able to: ability
We use be able to to express ability. "Able" is an
adjective meaning: having the power, skill or means to do something. If we say
"I am able to swim", it is like saying "I can
swim". We sometimes use "be able to" instead of "can"
or "could" for ability. "Be able to" is possible in all
tenses—but "can" is possible only in the present and
"could" is possible only in the past for ability. In addition,
"can" and "could" have no infinitive form. So we use
"be able to" when we want to use other tenses or the infinitive. Look at these examples:
I have been able to swim since I was five. (present perfect)
You will be able to speak perfect English very
soon. (future simple)
I would like to be able to fly an airplane. (infinitive)
Have To (objective obligation)
We often use have to to say that something is obligatory, for
example:
Children have to go to school.
Structure of Have To
"Have to" is often grouped with modal auxiliary verbs for
convenience, but in fact it is not a modal verb. It is not even an
auxiliary verb. In the "have to" structure, "have" is a main
verb. The structure is:
subject + auxiliary verb + have + infinitive
(with "to")
Look at these examples in the simple tense:
subject
auxiliary verb
main verb
"have"
infinitive (with
"to")
+
She
has
to work.
-
I
do not
have
to see
the doctor.
?
Did
you
have
to go
to school?
Use of Have To
In general, "have to" expresses impersonal obligation. The
subject of "have to" is obliged or forced to act by a separate,
external power (for example, the Law or school rules). "Have
to" is objective. Look at these examples:
In France, you have to drive on the right.
In England, most schoolchildren have to wear a
uniform.
John has to wear a tie at work.
In each of the above cases, the obligation is not the subject's opinion or
idea. The obligation is imposed from outside.
We can use "have to" in all tenses, and also with modal
auxiliaries. We conjugate it just like any other main verb. Here are some
examples:
subject
auxiliary verb
main verb "have"
infinitive
past simple
I
had
to work
yesterday.
present simple
I
have
to work
today.
future simple
I
will
have
to work
tomorrow.
present continuous
She
is
having
to wait.
present perfect
We
have
had
to change
the time.
modal (may)
They
may
have
to do
it again.
Must (subjective obligation)
We often use must to say that something is essential or necessary,
for example:
I must go.
Structure of Must
"Must" is a modal auxiliary verb. It is followed by a main verb.
The structure is:
subject + must + main verb
The main verb is the base verb (infinitive without "to").
Look at these examples:
subject
auxiliary
verb
"must"
main
verb
I
must
go
home.
You
must
visit
us.
We
must
stop
now.
Use of Must
In general, "must" expresses personal obligation.
"Must" expresses what the speaker thinks is necessary. "Must" is subjective. Look at these examples:
I must stop smoking.
You must visit us soon.
He must work harder.
In each of the above cases, the "obligation" is the opinion or
idea of the person speaking. In fact, it is not a real obligation. It is not
imposed from outside.
We can use "must" to talk about the present or the future.
Look at these examples:
I must go now. (present)
I must call my mother tomorrow. (future)
There is no past tense for "must". We use
"have to" to talk about the past.
Must Not (prohibition)
We use must not to say that something is not permitted or allowed,
for example:
Passengers must not talk to the driver.
Structure of Must Not
"Must" is an auxiliary verb. It is followed by a main
verb. The structure for "Must Not" is:
Subject + "Must Not" + Main Verb
The Main Verb is the base verb (infinitive without "to").
"Must Not" is often contracted to "mustn't".
Look at these examples:
subject
auxiliary
"Must" + "Not"
main
verb
I
mustn't
forget
my keys.
You
mustn't
disturb
him.
Students
must
not
be
late.
NB: like all auxiliary verbs, "must" cannot be
followed by an infinitive. So, we say:
You mustn't arrive late. (not You mustn't to
arrive late.)
Use of Must Not
"Must Not" expresses prohibition - something that is not
permitted, not allowed. The prohibition can be subjective (the speaker's
opinion) or objective (a real law or rule). Look at these
examples:
I mustn't eat so much sugar. (subjective)
You mustn't watch so much television. (subjective)
Students must not leave bicycles here. (objective)
Policemen must not drink on duty. (objective)
We use "Must Not" to talk about the present or the future:
Visitors must not smoke. (present)
I mustn't forget Tara's birthday. (future)
We cannot use "Must Not" for the past. We use another
structure to talk about the past, for example:
We were not allowed to enter.
I couldn't park outside the shop.
Shall and Will
People may sometimes tell you that there is no difference between shall
and will, or even that today nobody uses shall (except in offers
such as "Shall I call a taxi?"). This is not really true. The
difference between shall and will is often hidden by the fact
that we usually contract them in speaking with 'll. But the difference
does exist.
The truth is that there are two conjugations for the verb will:
1st Conjugation (objective, simple statement of fact)
Person
Verb
Example
Contraction
Singular
I
shall
I shall be in London tomorrow.
I'll
you
will
You will see a large building on the left.
You'll
he, she, it
will
He will be wearing blue.
He'll
Plural
we
shall
We shall not be there when you arrive.
We shan't
you
will
You will find his office on the 7th floor.
You'll
they
will
They will arrive late.
They'll
2nd Conjugation (subjective, strong assertion, promise
or command)
Person
Verb
Example
Contraction
Singular
I
will
I will do everything possible to help.
I'll
you
shall
You shall be sorry for this.
You'll
he, she, it
shall
It shall be done.
It'll
Plural
we
will
We will not interfere.
We won't
you
shall
You shall do as you're told.
You'll
they
shall
They shall give one month's notice.
They'll
It is true that this difference is not universally recognized. However, let
those who make assertions such as "Americans never use 'shall'"
peruse a good American English dictionary, or many American legal documents,
which often contain phrases such as:
Each party shall give one month's notice in writing
in the event of termination.
Note that exactly the same rule applies in the case of should and would. It
is perfectly normal, and somewhat more elegant, to write, for example:
·
I should be grateful if you would kindly send me
your latest catalogue.
Ten sentences:
1)
Children have to go to school.
2)
I must go to the university.
3)
People mustn’t drive a car when
they drink alcohol.
4)
I needn’t do math today, I can do
it later.
5)
I should study harder before
exams.
6)
Elephants and mice can’t fly.
7)
I could play snooker much better
two years ago than I can now.
8)
I can’t have made a mistake
in my calculations because I used a calculator.
9)
Can you run 100 meters in 5.5
seconds? 10)
10)Students
mustn’t eat or drink during the lection.
Texts:
Combinatorial mathematics.
Specialists in a broad range
of fields have to deal with problems that involve combinations made up
of letters, numbers or any other objects.
The
field of mathematics that studies problems of how many different combinations can
be built out of a specific number of objects is called combinatorial
mathematics (combinatorics).
This
branch of mathematics has its origin in the 16th century, in the
gambling games that played such a large part in high society in those times.
These games gave the initial impetus to develop combinatorial mathematics and
the theory of probability.
Italian
and French mathematicians were the first to enumerate the various combinations
achieved in games of dice. Further advances in the theory of combinations were
connected with the names of German scientists.
In
recent years combinatorial mathematics has seen extensive developments
associated with grater interest in problems of discrete mathematics.
Combinatorial methods can be employed in solving transport problems, in
particular scheduling; the scheduling of production facilities and of the sale
of goods. Links have been established between combinatorics and problems of
linear programming, statistics, etc. Combinatorial methods are used in coding
and decoding and in the solution of other problems of information theory.
The
combinatorial approach also plays a significant role in purely mathematical
problems such as the theory of groups and their representations, in the study
of the main principles of geometry, some branches of algebra, etc.
Probability.
Probability
is a mathematical expression of the likelihood of an event. Every probability
is a fraction. The largest probability can be 1. The smallest
probability can be is 0, meaning that it’s something that cannot
happen. You can find the probability that something will not
happen by subtracting the probability that it will happen from 1. For
example, if the weatherman tells you that there is a 0.3 probability of rain
today, then there must be a 0.7 probability that it won’t rain.
