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.

Sample questions

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

   1. ∃
   2. ∀
   3. ∈
   4. ∉
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   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
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   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
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   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
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   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
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   Answer: A. ∀x ∈ A, x ∈ B

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

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