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Solved problems for the chapter:

Logic

View the theory »

Infinite sequence

1. Near point

2. Infinite sequence limit

2.1. Convergence sequence

2.2. Divergent sequence

2.3. Limit of a sequence

3. Evaluation of limits

3.1. Euler's number

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:logic/5564/

Example 1.

Write down the given values in intervals and then calculate:

Example 2.

Determine when the statement below can be evaluated to be true.

Calculate the value of the statement:

if statements are made

Determine when the statement below can be evaluated to be true.

Write down each of the given sets in interval notation and then obtain:

Indicate the order of calculation in parentheses in the given statement.

10.

Indicate the order of calculation in parentheses in the given statement.

11.

Write the given statement with symbols.

Proposition:

Lines lying in a plane are parallel or intersect.

12.

Write the given statement with symbols.

Proposition:

The product of two numbers is positive only when both factors are positive or both factors are negative.

13.

Write the given statement with symbols.

Declaration:

Integers are only the same when their difference is 0.

14.

Write the given statement with symbols.

Proposition:

The integer a is greater than b if and only if .

15.

Write the given statement with symbols.

Proposition:

The integer a is less than b if and only if a - b <0.

16.

Write the given statement with symbols.

Proposition: Let a, b and c be from the set of integers. If the number a is less than b, then .

17.

Write the given statement with symbols.

Proposition: Let a and b be from the set of integers. If a is less than or equal to b and b is less than or equal to a, then the numbers a and b are equal.

18.

Write the given statement with symbols.

Proposition: Let a, b and c be from the set of integers. If a is less than or equal to b and b is less than or equal to c, then a is less than or equal to c.

19.

Write the given statement with symbols.

Proposition: When multiplying the inequality of two integers by a positive number, the sign of the inequality is preserved.

20.

Write the given statement with symbols.

Proposition: When multiplying the inequality of two integers by a negative number, the inequality sign is reversed.

21.

Determine the correctness of the given statement.

22.

Determine the correctness of the given statement.

23.

Determine the correctness of the given statement.

24.

Determine the correctness of the given statement.

25.

Determine the correctness of the given statement.

The conjunction of two statements is correct when the statements have the same value.

26.

Determine the correctness of the given statement.

Declarations and can be both incorrect at the same time .

27.

Determine the correctness of the given statement.

If the statement A is correct and the statement B is incorrect (the condition is correct and the consequence is incorrect) the implication of the statements A and B is incorrect.