Intermediate
Discrete Mathematics & Math
Q80 / 100
What is the negation of the statement "For all x, there exists a y such that x + y = 0"?
Correct! Well done.
Incorrect.
The correct answer is B) There exists an x such that for all y, x + y ≠ 0
B
Correct Answer
There exists an x such that for all y, x + y ≠ 0
Explanation
Negating ∀x∃y P(x,y) flips each quantifier and negates the predicate, giving ∃x∀y ¬P(x,y): "There exists an x such that for all y, x + y ≠ 0." This quantifier-negation rule (∀↔∃ swap with inner negation) is essential for writing correct proofs and counterexamples.
Progress
80/100