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MAT Sets Basics — practice questions

Explore 35 free Sets Basics questions in MAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sets Basics questions and exercises with answers

Showing questions 1–30 of 35.

The set A = {x : x is a natural number, 1 < x < 2} isRead the answer and worked solution →Which of the following sets is INFINITE?Read the answer and worked solution →Writing the set {x : x is an integer and −3 ≤ x < 7} in roster form givesRead the answer and worked solution →The number of distinct elements of the set A formed by the letters of the word 'LOYAL' isRead the answer and worked solution →Which symbol is used to denote 'is an element of' in set notation?Read the answer and worked solution →Let A = {1, 2, 3, 4, 5, 6}. Which of the following statements is correct?Read the answer and worked solution →Which of the following pairs of sets is equal?Read the answer and worked solution →Which of these is an EXAMPLE of the null set?Read the answer and worked solution →The set-builder form of the set {3, 6, 9, 12} can be written asRead the answer and worked solution →If A and B are two sets such that every element of A is in B and every element of B is in A, thenRead the answer and worked solution →The number n(S) of distinct elements of the set S formed by the letters of the word 'TRIGONOMETRY' isRead the answer and worked solution →Consider C = {x : x − 5 = 0} and E = {x : x is an integral positive root of x² − 2x − 15 = 0}. ThenRead the answer and worked solution →Let A = {n : n ∈ ℤ and n² ≤ 4} and B = {x : x ∈ ℝ and x² − 3x + 2 = 0}. ThenRead the answer and worked solution →Which of the following statements is INCORRECT?Read the answer and worked solution →Set A is defined as {x : x is an integer, x² ≤ 4}. Which is the correct roster of A?Read the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →

Worked practice questions

The set A = {x : x is a natural number, 1 < x < 2} is

  1. A finite set with one element
  2. An infinite set
  3. The empty set
  4. Equal to {1, 2}
Show answer and solution

Correct answer: C. The empty set

There is no natural number strictly between 1 and 2, so A is empty (denoted φ or { }).

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Which of the following sets is INFINITE?

  1. The set of months of a year
  2. {1, 2, 3, …, 99, 100}
  3. The set of positive integers greater than 100
  4. The set of prime numbers less than 99
Show answer and solution

Correct answer: C. The set of positive integers greater than 100

There is no upper bound on the positive integers greater than 100, so it is infinite. The other three each contain a finite, definite count of elements.

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Writing the set {x : x is an integer and −3 ≤ x < 7} in roster form gives

  1. {−2, −1, 0, 1, 2, 3, 4, 5, 6}
  2. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8}
  3. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6}
  4. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7}
Show answer and solution

Correct answer: C. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6}

The inequality includes −3 (≤) and excludes 7 (strict <), giving the integers −3, −2, −1, 0, 1, 2, 3, 4, 5, 6.

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More Mathematics topics

Binomial TheoremSequences and SeriesGeometryProbability & StatisticsSequencesPermutations and CombinationsSequences and Series GpCorrelation and Regression