Question

[-3;1)~(0;4] equals to:

a. (0;1)
b. [0;1]
c. [-3;4]
d. [3;0]

Answer 1

c. [-3, 4]

Explanation:

The expression [-3;1) U (0; 4] in set notation represents the union of the two intervals.

Interval [-3;1)

This interval includes all real numbers that are greater than or equal to -3 (denoted by the square bracket) and less than 1 (denoted by the parenthesis). In set notation, this interval can be expressed as:

• 
  `\large\text{$\x\; $}`

Interval (0; 4]

This interval includes all real numbers that are greater than 0 (denoted by the parenthesis) and less than or equal to 4 (denoted by the square bracket). In set notation, this interval can be expressed as:

• 
  `\large\text{$\x\; $}`

The union of two sets is a new set that contains all the unique elements from both of the original sets, ensuring that each element appears only once in the resulting set.

So, when we take the union of these two intervals, the set includes all real numbers that are greater than or equal to -3 and less than or equal to 4:

• 
  `\Large\text{$[-3, 4]$}`

Answer 2

c. [-3;4]

Explanation:

The union of two intervals is the set of all numbers that are in either interval or in both intervals.

The interval [-3;1) includes all numbers from -3 up to and not including 1.

The interval [0;4] includes all numbers from 0 up to and including 4.

Therefore, the union of these two intervals is the set of all numbers from -3 up to and including 4.

This can be written mathematically as [-3;4].

Therefore, answer is: c. [-3;4]