Practice Quantifiers in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Symbols specifying the scope of a predicate: \forall (for all, universal) and \exists (there exists, existential).
\forall means 'for all' (everyone). \exists means 'there exists' (at least one).
Example 1
easyTranslate into symbols and determine the truth value: (a) 'Every natural number is positive.', (b) 'There exists a real number x such that x^2 = 2.'
Example 2
mediumNegate the statement \forall x \in \mathbb{R},\; x^2 \ge 0 and determine the truth value of both the original and its negation.
Example 3
easyWrite in words: (a) \forall x \in \mathbb{Z},\; x + 0 = x, (b) \exists x \in \mathbb{N},\; x < 5.
Example 4
mediumDetermine the truth value of each and write its negation: (a) \forall x \in \mathbb{R},\; x > 0, (b) \exists x \in \mathbb{Z},\; x^2 = 3.