LT

Test: Sets and absolute value

This test covers union, intersection and difference of sets and their representation with Venn diagrams. Absolute-value tasks develop interpretation as distance on a number line, equation solving and reasoning about real numbers.

Question qty: 10
Duration in minutes: 13
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Sample questions

  • Solve |x| = a.
  • Calculate |x|.
  • Calculate √((a)²).
  • Numbers a and b are marked on a number line. What is their distance?
  • A ∪ B has u elements, A has a, and B has b. How many are in A ∩ B?
  • Set A has a elements, B has b, and their intersection has i. How many are in A ∪ B?
  • A has a elements and A ∩ B has i. How many are in A \ B?
  • What does the intersection A ∩ B mean?

Sets and absolute value

A set can be specified by listing its elements or by a defining property. The union A ∪ B contains elements in at least one set, the intersection A ∩ B those in both, and the difference A B those in A but not B.

Absolute value and distance

The absolute value |x| is the distance from zero and is therefore non-negative. For a > 0, |x| = a gives x = a or x = −a. The inequality |x| < a describes points between −a and a, while |x| > a describes points outside. Include endpoints only when the inequality permits equality.

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