Quantifiers Quiz - CBSE Class 11 Mathematics

Free practice quiz: Quantifiers (CBSE Class 11 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 11 Mathematics practice quiz has 18 multiple-choice questions on Quantifiers, and 18 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Which quantifier means 'for all' or 'for every'?

   1. ∃
   2. ∀
   3. ∈
   4. ∉
   Show answer

   Answer: B. ∀

   The universal quantifier ∀ means 'for all' or 'for every'.

2. Is the statement '∃x ∈ ℝ, x² < 0' true or false?

   1. True
   2. False
   Show answer

   Answer: B. False

   The statement is false because there is no real number whose square is negative.

3. Negate the statement '∃x ∈ ℤ, x is even'.

   1. ∃x ∈ ℤ, x is odd
   2. ∀x ∈ ℤ, x is odd
   3. ∃x ∈ ℤ, x is not even
   4. ∀x ∈ ℤ, x is not even
   Show answer

   Answer: D. ∀x ∈ ℤ, x is not even

   The negation of an existential quantifier is a universal quantifier, and the negation of 'x is even' is 'x is not even'.

4. Consider the statement: 'For every real number x, there exists a real number y such that x + y = 0'. Write this statement symbolically using quantifiers.

   1. ∀x ∈ ℝ, ∃y ∈ ℝ, x + y = 0
   2. ∃x ∈ ℝ, ∀y ∈ ℝ, x + y = 0
   3. ∀x ∈ ℝ, ∀y ∈ ℝ, x + y = 0
   4. ∃x ∈ ℝ, ∃y ∈ ℝ, x + y = 0
   Show answer

   Answer: A. ∀x ∈ ℝ, ∃y ∈ ℝ, x + y = 0

   The statement correctly uses the universal quantifier (∀) for x and the existential quantifier (∃) for y, reflecting the order of the statement.

5. Let A and B be sets. Write the statement 'Every element of A is an element of B' using quantifiers.

   1. ∀x ∈ A, x ∈ B
   2. ∃x ∈ A, x ∈ B
   3. ∀x ∈ B, x ∈ A
   4. ∃x ∈ B, x ∈ A
   Show answer

   Answer: A. ∀x ∈ A, x ∈ B

   The statement means 'for all x in A, x is in B'.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Which quantifier means 'there exists'?
2. Is the statement '∀x ∈ ℝ, x² ≥ 0' true or false?
3. Translate the statement 'All integers are rational numbers' into symbolic form using quantifiers.
4. Translate the statement 'There exists a prime number greater than 100' into symbolic form using quantifiers.
5. Negate the statement '∀x ∈ ℝ, x > 0'.
6. Determine the truth value of the statement: '∃n ∈ ℤ⁺ such that n² = 2n'.
7. Let P(x) be the statement 'x is divisible by 3'. What is the negation of the statement ∃x ∈ ℤ, P(x)?
8. What is the negation of the statement: '∀ε > 0, ∃δ > 0 such that if 0 < |x - a| < δ, then |f(x) - L| < ε'?
9. Prove or disprove: ∀x ∈ ℝ, ∃y ∈ ℝ such that xy = 1.
10. Prove or disprove: ∃x ∈ ℝ such that ∀y ∈ ℝ, x + y = y.
11. Let f: ℝ → ℝ be a function. Write the statement 'f is injective' using quantifiers.
12. Formulate a statement using quantifiers that is equivalent to the statement: 'There are no irrational numbers that are also rational numbers'.
13. Is the following statement true or false? 'There exists a real number x such that for all real numbers y, x + y = 0'.

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