Worksheet: Intervals

In this worksheet, we will practice determining limited and unlimited intervals.

Q1:

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

  • A[3,1]
  • B[3,1)
  • C(3,1)
  • D(3,1]

Q2:

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

  • A(0,)
  • B(,0)
  • C(,1)
  • D(1,)
  • E(,)

Q3:

Which of the following is true?

  • A16(4,)
  • B16(4,)
  • C16(4,)
  • D16(4,)

Q4:

Which of the following is a half-open interval?

  • A{1,9}
  • B[1,9]
  • C(1,9)
  • D[1,9)

Q5:

Given that 𝑋=[8,3) and 𝑌=[4,3), find 𝑋𝑌.

  • A[4,3)
  • B[8,4)[3,3)
  • C[8,3)
  • D

Q6:

Given that 𝑋=(3,4] and 𝑌=[6,2), find 𝑋𝑌.

  • A(3,4]
  • B[6,2)
  • C[6,4]
  • D

Q7:

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

  • A[4,1]
  • B(4,1)
  • C[4,1)
  • D(,4][1,)
  • E(4,1]

Q8:

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

  • A{2,4}
  • B(2,4]
  • C[2,4]
  • D[2,4)
  • E(2,4)

Q9:

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

  • A(a)
  • B(b)
  • C(d)
  • D(c)

Q10:

Given that 𝑋=[7,2] and 𝑌=(2,), find 𝑌𝑋.

  • A(2,)
  • B
  • C[7,2]
  • D[7,)

Q11:

What is [5,4]?

  • A(0,4]
  • B[5,4]
  • C[5,0]
  • D[5,0)

Q12:

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

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q13:

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

  • A𝑋={𝑥6<𝑥<3,𝑥}
  • B𝑋={𝑥6<𝑥3,𝑥}
  • C𝑋={𝑥6𝑥<3,𝑥}
  • D𝑋={𝑥6𝑥3,𝑥}

Q14:

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

  • A(4,1){3}
  • B[4,3){1}
  • C(4,3){1}
  • D(4,3]{1}
  • E[4,3]{1}

Q15:

Express the following set using interval notation: 𝑋=𝑥𝑥8,𝑥.

  • A[2,)
  • B(2,)
  • C(,2]
  • D(,2)

Q16:

If 𝑥[1,625), what interval is 𝑥 in?

  • A[0,25)
  • B[1,25)
  • C[25,1)
  • D[1,25)
  • E[1,0)

Q17:

Given that (,𝑘)[22,11]=[22,9), determine the value of 𝑘.

Q18:

Which of the following sets satisfies (17,15]𝑋=[20,15]?

  • A𝑋=(20,18)
  • B𝑋=[17,16]
  • C𝑋=(17,16)
  • D𝑋=[20,16]
  • E𝑋=[20,17)

Q19:

Which of the following sets satisfies [15,0]𝑋=(15,0)?

  • A𝑋=(15,0)
  • B𝑋={15,0}
  • C𝑋=(15,0]
  • D𝑋=
  • E𝑋=[15,0)

Q20:

Which of the following is true?

  • A163(9,5)
  • B163(9,5)
  • C163(9,5)
  • D163(9,5)

Q21:

Given that 𝑋=(6,6) and 𝑌={6,1}, find 𝑋𝑌.

  • A(6,6)
  • B{1}
  • C[6,6)
  • D{6,1}

Q22:

Which of the following is true?

  • A1[1,)
  • B1[1,)
  • C1[1,)
  • D1[1,)

Q23:

Which of the following is true?

  • A(2,7)(,9]
  • B(2,7)(,9]
  • C(2,7)(,9]
  • D(2,7)(,9]

Q24:

Given that 𝑋=[6,3] and 𝑌={4,3}, find 𝑋𝑌.

  • A[6,3]
  • B[6,4)(4,3)
  • C{4,3}
  • D{4}

Q25:

Which of the following is true?

  • A|12|(11,15)
  • B|12|(11,15)
  • C|12|(11,15)
  • D|12|(11,15)

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