Applied Informatics RFET MTT 1102 Mathematics

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Uploaded: 06.12.2016
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The content of the questions which were answered:
Check of knowledge. sets
Check of knowledge. Sayings
Check of knowledge. Formulas of propositional algebra
Check of knowledge. Predicates
Check of knowledge. Binary relations
Check of knowledge. display concept
Mandatory evaluation of the course Essay
 
Responses to 100%
 
Check of knowledge. sets
Exercise 1
Specify the cardinality of A.
1. A - the set of letters of the Latin alphabet
2. A = {a, b, c, 1,2,3}
3. A = B × CA = B × C, where B = {a, b, c} B = {a, b, c} and C = {1,2,3}
4. A = B × CA = B × C, where | B | = 4 | B | = 4 and | C | = 5
 
Task 2
Find the Cartesian product A × B of sets A and B.
1. A = {a, b, c}; B = {b, e} A = {a, b, c}; B = {b, e}.
{(B, a), (e, a), (e, b), (b, b), (b, c), (e, c)} {(b, a), (e, a), (e, b), (b, b), (b, c), (e, c)}
{(A, b), (a, e), (b, e), (b, b), (c, b)} {(a, b), (a, e), (b, e), (b, b), (c, b)}
{(A, b), (a, e), (b, e), (b, b), (c, b), (c, e), (b, a), (e, a), ( e, b), (b, b), (b, c), (e, c)} {(a, b), (a, e), (b, e), (b, b), (c , b), (c, e), (b, a), (e, a), (e, b), (b, b), (b, c), (e, c)}
{(A, b), (b, e), (a, e), (c, b), (c, e), (b, b)}
 
2. A = {1,2}; B = {a, b, c} A = {1,2}; B = {a, b, c}.
3. A = {x: 1≤x <2}; B = {x: 2 <x≤3} A = {x: 1≤x <2}; B = {x: 2 <x≤3}.
 
Check of knowledge. Sayings
Exercise 1
Select all the true statements:
Moscow - the capital of Russia and Moscow has less than 1 million inhabitants.
It is not true that 5> 8
If 6 is a prime number, then 20 - prime number
5 8> 8 or> 5
Invalid following statement: 5> 88 8 or> 5
If 3 is a prime number, then 6 - prime number
 
Task 2
Which of the following statements are statements?
Kursk has more than one million inhabitants.
x = 5x = 5.
The Russian alfivite 33 letters.
Madrid - the capital of Japan.
What month is it?
Number 8 is simple.
23-1.
Buy this CD.
 
Check of knowledge. Formulas of propositional algebra
Exercise 1
Which of the following expressions are formulas of propositional algebra?
C↔
(A∧B) → C
(A∨C) → C
(A∧B¯¯¯¯) ↔C
(A∨B) → C
A B
Task 2
Taking into account the priorities of the logical signs, lower brackets, where possible, in the formulas.
(A∧B) → (A∨B)
 
Activity 3
Given the statements A and B. Costavte of the statements A and B compound statement X such that:
1 X is true if and only if the statement is true and B is false statement A.
B → A
A → B
A → B
B → A
 
Activity 4
Given the statements A, B, CPostroit of these statements saying X such that:
X is true if and only if the truth of all propositions A, B, C
 
Task 5
Is this formula is identically true identically false, doable?
(A∧B) → (A∨B)
identically true
doable
false identity
 
Check of knowledge. Predicates
Exercise 1
Determine the truth of these statements, under the condition that the x, y, z∈R.
∃x ∃y x + y = 2
verily
falsely
 
 
Task 2
Determine whether the following statements or suggestions n-ary predicates. All variables belong to the set of real numbers.
 
Check of knowledge. Binary relations
Exercise 1
Given a set A = {a, b, c, d, e, f, g, h} A = {a, b, c, d, e, f, g, h} and the set of subsets A1 = {a, b, d}, A2 = {a, c, e, f}, A3 = {f, g, h}, A4 = {c, g, h}, A5 = {c, f, g}, A1 = {a, b, d}, A2 = {a, c, e, f}, A3 = {f, g, h}, A4 = {c, g, h}, A5 = {c, f, g}, A6 = { e, f}, A7 = {a, e, f} A6 = {e, f}, A7 = {a, e, f}
Note the set belonging to the partition of A.
A4
A2
A1
A6
A5
A3
A7
 
Task 2
On the set of MM given binary relation RR. Determine which of the following conditions: reflexivity, symmetry, transitivity, antisymmetry - RR has attitude.
 
M - the set of all people, a R ba R b if and only if aa born in the same year with bb
reflexivity
symmetry
transitivity
antisymmetry
 
Check of knowledge. di

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