Set Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Write the set B={x∈Z:−2≤x<3}B = \{x \in \mathbb{Z} : -2 \le x < 3\} in roster notation.

Solution

  1. 1
    Parse the set-builder notation B={x∈Z:−2≤x<3}B = \{x \in \mathbb{Z} : -2 \le x < 3\}: we need all integers xx satisfying −2≤x-2 \le x AND x<3x < 3.
  2. 2
    List integers from −2-2 upward, stopping before 3: −2,−1,0,1,2-2, -1, 0, 1, 2. The integer 3 is excluded because the condition is strict (x<3x < 3).
  3. 3
    Write in roster form: B={−2,−1,0,1,2}B = \{-2, -1, 0, 1, 2\}. Verify: ∣B∣=5|B| = 5 elements, consistent with the range from −2-2 to 22 inclusive.

Answer

B={−2,−1,0,1,2}B = \{-2, -1, 0, 1, 2\}
Set-builder notation describes elements by a property. Converting to roster notation means listing every element that satisfies the condition explicitly.

About Set

A well-defined collection of distinct, unordered objects called elements, described either by listing or by a membership rule.

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More Set Examples

Example 1 easy

Let [formula]. Determine whether [formula] and whether [formula].

Example 3 easy

Let [formula]. List all elements of [formula] and state the cardinality [formula].

Example 4 easy

Are the sets [formula] and [formula] equal? Explain.

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