Practice question · Select all that apply
Select every statement that is TRUE.
Hints
- The chain of inclusions runs one way only: naturals inside integers inside rationals inside reals.
- For each claim, either it follows from the nesting or you can name a counterexample.
Show the answer
- B. Every integer is a rational number
- C. Every natural number is a real number
- F. Some rational numbers are not integers
Why
Inclusion runs upward, never downward: 5 = 5/1 is rational, and every natural is real. But 1/2 refutes 'every rational is an integer', and the square root of 2 refutes 'every real is rational'. Reversing a nesting is the classic error here.
Practise Number Systems
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