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Sagot :
Let's analyze each statement individually to determine if it is true or false:
1. Statement: [tex]\(2 \leq 2\)[/tex]
- Here, we check if 2 is less than or equal to 2. Since 2 is equal to 2, this statement is true.
- Result: True
2. Statement: [tex]\(-2 \geq -2.5 \geq -3\)[/tex]
- This is a compound inequality. First, we check [tex]\(-2 \geq -2.5\)[/tex]. Since [tex]\(-2\)[/tex] is greater than [tex]\(-2.5\)[/tex], the first part is true.
- Next, we check [tex]\(-2.5 \geq -3\)[/tex]. Since [tex]\(-2.5\)[/tex] is greater than [tex]\(-3\)[/tex], the second part is true as well.
- Since both parts are true, the entire compound inequality is true.
- Result: True
3. Statement: [tex]\(10000 > -1000000\)[/tex]
- We need to determine if [tex]\(10000\)[/tex] is greater than [tex]\(-1000000\)[/tex]. This is evidently true since [tex]\(10000\)[/tex] is a large positive number and [tex]\(-1000000\)[/tex] is a large negative number.
- Result: True
4. Statement: [tex]\(2 = 2\)[/tex]
- Here, we verify if [tex]\(2\)[/tex] is equal to [tex]\(2\)[/tex]. This is directly true as both sides of the equation match.
- Result: True
5. Statement: [tex]\(2 \geq 2\)[/tex]
- We check if [tex]\(2\)[/tex] is greater than or equal to [tex]\(2\)[/tex]. Since [tex]\(2\)[/tex] is equal to [tex]\(2\)[/tex], this statement is true.
- Result: True
6. Statement: [tex]\(-2 \leq -2.5 \leq -3\)[/tex]
- This is another compound inequality. First, we check [tex]\(-2 \leq -2.5\)[/tex]. Since [tex]\(-2.5\)[/tex] is less than [tex]\(-2\)[/tex], this is false.
- For the second part, [tex]\(-2.5 \leq -3\)[/tex], it is false since [tex]\(-2.5\)[/tex] is not less than or equal to [tex]\(-3\)[/tex].
- Because the first part of the statement is false, the entire compound inequality is false.
- Result: False
7. Statement: [tex]\(-4 < 1\)[/tex]
- We need to determine if [tex]\(-4\)[/tex] is less than [tex]\(1\)[/tex]. This is clearly true since [tex]\(-4\)[/tex] is a negative number and [tex]\(1\)[/tex] is a positive number.
- Result: True
In summary, here are the results for each statement:
1. [tex]\(2 \leq 2\)[/tex] is True
2. [tex]\(-2 \geq -2.5 \geq -3\)[/tex] is True
3. [tex]\(10000 > -1000000\)[/tex] is True
4. [tex]\(2 = 2\)[/tex] is True
5. [tex]\(2 \geq 2\)[/tex] is True
6. [tex]\(-2 \leq -2.5 \leq -3\)[/tex] is False
7. [tex]\(-4 < 1\)[/tex] is True
1. Statement: [tex]\(2 \leq 2\)[/tex]
- Here, we check if 2 is less than or equal to 2. Since 2 is equal to 2, this statement is true.
- Result: True
2. Statement: [tex]\(-2 \geq -2.5 \geq -3\)[/tex]
- This is a compound inequality. First, we check [tex]\(-2 \geq -2.5\)[/tex]. Since [tex]\(-2\)[/tex] is greater than [tex]\(-2.5\)[/tex], the first part is true.
- Next, we check [tex]\(-2.5 \geq -3\)[/tex]. Since [tex]\(-2.5\)[/tex] is greater than [tex]\(-3\)[/tex], the second part is true as well.
- Since both parts are true, the entire compound inequality is true.
- Result: True
3. Statement: [tex]\(10000 > -1000000\)[/tex]
- We need to determine if [tex]\(10000\)[/tex] is greater than [tex]\(-1000000\)[/tex]. This is evidently true since [tex]\(10000\)[/tex] is a large positive number and [tex]\(-1000000\)[/tex] is a large negative number.
- Result: True
4. Statement: [tex]\(2 = 2\)[/tex]
- Here, we verify if [tex]\(2\)[/tex] is equal to [tex]\(2\)[/tex]. This is directly true as both sides of the equation match.
- Result: True
5. Statement: [tex]\(2 \geq 2\)[/tex]
- We check if [tex]\(2\)[/tex] is greater than or equal to [tex]\(2\)[/tex]. Since [tex]\(2\)[/tex] is equal to [tex]\(2\)[/tex], this statement is true.
- Result: True
6. Statement: [tex]\(-2 \leq -2.5 \leq -3\)[/tex]
- This is another compound inequality. First, we check [tex]\(-2 \leq -2.5\)[/tex]. Since [tex]\(-2.5\)[/tex] is less than [tex]\(-2\)[/tex], this is false.
- For the second part, [tex]\(-2.5 \leq -3\)[/tex], it is false since [tex]\(-2.5\)[/tex] is not less than or equal to [tex]\(-3\)[/tex].
- Because the first part of the statement is false, the entire compound inequality is false.
- Result: False
7. Statement: [tex]\(-4 < 1\)[/tex]
- We need to determine if [tex]\(-4\)[/tex] is less than [tex]\(1\)[/tex]. This is clearly true since [tex]\(-4\)[/tex] is a negative number and [tex]\(1\)[/tex] is a positive number.
- Result: True
In summary, here are the results for each statement:
1. [tex]\(2 \leq 2\)[/tex] is True
2. [tex]\(-2 \geq -2.5 \geq -3\)[/tex] is True
3. [tex]\(10000 > -1000000\)[/tex] is True
4. [tex]\(2 = 2\)[/tex] is True
5. [tex]\(2 \geq 2\)[/tex] is True
6. [tex]\(-2 \leq -2.5 \leq -3\)[/tex] is False
7. [tex]\(-4 < 1\)[/tex] is True
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