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: (for all, universal) and (there exists, existential).
means 'for all' (everyone). means 'there exists' (at least one).
Showing a random 20 of 50 problems.
Example 1
easyFill in: The negation of is ____.
Example 2
easyTrue or false over : is even.
Example 3
mediumFill in: is equivalent to . Fill the .
Example 4
challengeExpress 'there is exactly one with ' using , , and equality.
Example 5
easyIs '' true or false?
Example 6
easyTranslate into symbols and determine the truth value: (a) 'Every natural number is positive.', (b) 'There exists a real number such that .'
Example 7
mediumTranslate: 'The function is surjective from to ' using quantifiers.
Example 8
mediumDisprove '' by giving a counterexample or show it is true.
Example 9
mediumTranslate 'every integer is even or odd' and write its negation.
Example 10
easyWrite in words: (a) , (b) .
Example 11
mediumRewrite 'no real number satisfies ' with a quantifier, then give the equivalent universal form.
Example 12
challengeTranslate uniqueness '' using only .
Example 13
mediumTranslate, then determine truth over : 'For every positive real there is a positive real with .'
Example 14
hardOver , decide and justify: '.'
Example 15
easyTranslate 'every prime greater than is odd' into quantifier notation (let = ' is prime', ).
Example 16
mediumDetermine the truth value of each and write its negation: (a) , (b) .
Example 17
easyWhat does the symbol mean?
Example 18
hardTranslate 'there is no largest integer' two ways: (a) with , (b) with .
Example 19
easyFill in: The negation of is ____.
Example 20
easyWrite the negation of 'Every car in the lot is red' in plain English.