Practice question · Select all that apply
Select every statement that is a CORRECT negation of the one shown beside it.
Hints
- Negating 'all' gives 'at least one fails', not 'none'.
- The negation of 'greater than' must include the boundary case.
Show the answer
- A. 'Some x is prime' -> 'No x is prime'
- B. 'x > 3' -> 'x is at most 3'
- E. 'All swans are white' -> 'Some swan is not white'
Why
Correct negations: 'some swan is not white', 'no x is prime', and 'x is at most 3'. Option 2 overshoots (denying all does not assert none) and option 4 forgets x = 3, which satisfies neither 'x > 3' nor 'x < 3'.
Practise Proof by Contradiction and Contrapositive
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Proof by Contradiction and Contrapositive
- Order the steps of the classic proof by contradiction that the square root of 2 is irrational.
- Sort each opening line by the proof technique it belongs to.
- Euclid proved there are infinitely many primes by assuming a finite list and building N = p₁p₂…pₖ + 1. Why…
- Proof by contrapositive and proof by contradiction both begin by assuming a negation. What distinguishes…
- A conditional and its contrapositive always have the same truth value.