The negation

"In one side-street

There were houses.

In one of houses

Obstinate Thomas lives.

At houses, at school,

Anywhere, anybody —

Obstinate Thomas didn't believe

To anything."

It cite is from a child's poem «Thomas» by Sergey Mihalkov.

Thomas was, that is termed, expert of the critical analysis and he called all in question .

• «In the outdoors rain», — it is spoked to him. But Thomas respondedon this reasonable proposition on the usage:

• «Iniquity, there is no rain in the outdoors».

• «Look, — it is spoked to him in a Zoo, — It is the elephant».

But Thomas was correct to itself, he stated the negative proposition at once: «It's not the elephant».

From the point of view the logic Thomas to any proposition of the interlocutors applied logic operation of negation and did it primely: using a particle «not» or any proposition , equivalent to her, of a type «is insecure, that... »

If there is spoke him the truth, Thomas by such way converted the true proposition in false. And on the contrary: each false expression became true after such adding.

The outcome of the circumscribed linguistic handling is named as negation of the initial proposition.

The negation of any proposition names such statement, which one is false, when the initial proposition is true, and which one is true, when the initial proposition is false.

Negation is designated by sign “–”.

If proposition is designated as A, negation operation applied to A (not A, denial A) is designated as:

–A or ¬A or Ā or ~A or A′. It is read as “not A”.

Table for operation «not»

A	Not А		A	Not A
T	F	or	1	0
F	T		0	1

In the left column of the table the possible values of truth of the initial proposition are presented. Possibilities are only two: each proposition can be either true or false.

In a right column (as puts by Thomas) values of truth of negation of the initial proposition signs.

The conjunction (logical multiplication, logical “and”)

«Tomorrow on region will be rains and temperature will be reduced up to 10 degrees...»

Logic operation «AND» in this meteorological example hase a title of a conjunction. With its help from two propositions it obteins third, which one is true in only case when, when are true both initial propositions.

It is the definition of a conjunction:

With its help from two propositions it obtains third, which one is true in only case when, when are true both initial proposition

Or:

The new proposition obtained by application of this operation to initial propositions is named their conjunction.

Conjunction is designated as:

A&B or A Λ B or A·B or AB or A×B

It is read as “A and B”.

In a truth table for a conjunction of two propositions three columns present. In first two columns the truth values of the initial propositions are marked, in third column are marked value of their conjunction.

A (rain)	B (cold)	A and B
T	T	T
T	F	F
F	T	F
F	F	F

The analysis of a meteorological message had show, that among combinations of the initial propositions such are possible three, at which one their conjunction is false, and only one combination is those, that their conjunction is true. Total, four possibilities are as much rows in the table.

The logic operation of a conjunction allows to relate not only two, but also any final number of the propositions. Their conjunction is true in only case when, when each of them is true, she is false then, when one of them is false even.

Result of conjunction is true in only case when, when each of initial propositions is true, it is false then, when at least one of them is false.