Practice question · Sort into groups
Sort each object by whether it belongs to the set S = { x : x is an integer and x squared < 10 }.
Groups: In S · Not in S
- 4
- -3
- 0
- 3
- -4
- 1.5
Hints
- Two conditions must hold: being an integer, and squaring to less than 10.
- Squaring kills the minus sign, so negatives are not automatically excluded.
Show the answer
In S: 3, -3, 0
Not in S: 4, 1.5, -4
Why
S = {-3, -2, -1, 0, 1, 2, 3}. Both 3 and -3 square to 9 < 10, so both qualify. 4 and -4 square to 16, too big. And 1.5 fails the very first condition, it is not an integer, even though its square is only 2.25.
Practise Sets and Set-Builder Notation
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