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In this lesson, we will learn how to determine limited and unlimited intervals.

Q1:

The figure shows an interval on the number line. Write an expression for it using interval notation.

Q2:

Given that ] − ∞ , 𝑘 [ ∩ [ − 2 2 , 1 1 ] = [ − 2 2 , 9 [ , determine the value of 𝑘 .

Q3:

Which of the following sets satisfies ] − 1 7 , − 1 5 ] ∪ 𝑋 = [ − 2 0 , − 1 5 ] ?

Q4:

Express the set of real numbers ℝ in the form of an interval.

Q5:

Which of the following is true?

Q6:

Q7:

Q8:

Given that 𝑋 = [ − 8 , 3 [ and 𝑌 = [ − 4 , − 3 [ , find 𝑋 ∩ 𝑌 .

Q9:

Given that 𝑋 = ] − 6 , 5 [ and 𝑌 = ] 5 , 8 [ , find 𝑋 ∩ 𝑌 .

Q10:

Given that 𝑋 = ] − 3 , 4 ] and 𝑌 = [ − 6 , − 2 [ , find 𝑋 ∪ 𝑌 .

Q11:

Given that 𝑋 = [ − 3 , − 1 [ and 𝑌 = [ 0 , 8 ] , find 𝑋 ∪ 𝑌 .

Q12:

State the interval that is represented by the following number line.

Q13:

Q14:

Given that 𝑋 = [ − 7 , 2 ] and 𝑌 = ] 2 , ∞ [ , find 𝑌 − 𝑋 .

Q15:

Which of the following is a closed interval?

Q16:

What is [ − 5 , 4 ] ∩ ℝ ?

Q17:

Given that 𝑥 ∈ [ − 3 5 , ∞ [ , which of the following inequalities holds?

Q18:

Which of the following expressions represents the set shown on the number line?

Q19:

The figure shows an interval on the number line. Write an expression for the interval using set notation.

Q20:

Q21:

Which of the following figures represents the interval ] − 1 , 0 ] ?

Q22:

Q23:

Express the following set using interval notation: 𝑋 = 𝑥 ∶ 𝑥 ≤ √ − 8 , 𝑥 ∈ ℝ 3 .

Q24:

If 𝑥 ∈ [ 1 , 6 2 5 ) , what interval is − √ 𝑥 in?

Q25:

Which of the following figures represents the set ℝ − [ − 2 , 4 ] ?

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