(A) Two sets are disjoint if their intersection is the empty set,denoted by $\varnothing$.Let $A = \{ x : x \text{ is an even integer} \}$ and $B = \{

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(A) Two sets are disjoint if their intersection is the empty set,denoted by $\varnothing$.Let $A = \{ x : x \text{ is an even integer} \}$ and $B = \{ x : x \text{ is an odd integer} \}$.The intersection of $A$ and $B$ is given by:$A \cap B = \{ x : x \text{ is an even integer and } x \text{ is an odd integer} \}$.Since no integer can be both even and odd,$A \cap B = \varnothing$.Therefore,the pair of sets $A$ and $B$ is disjoint.

Class 11 Mathematics Set Theory Basic of Set theory

Easy

Which of the following pairs of sets are disjoint?
$A = \{ x : x \text{ is an even integer} \}$
$B = \{ x : x \text{ is an odd integer} \}$

A
$A$ and $B$ are disjoint
B
$A$ and $B$ are not disjoint
C
$A$ is a subset of $B$
D
$B$ is a subset of $A$

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Write the following set in roster form:
$A = \{ x : x \text{ is an integer and } -3 < x < 7 \}$

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If a set $A$ has $n$ elements,then the total number of subsets of $A$ is

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Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

$(i)$ $\{1, 2, 3, 6\}$ $(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$

$(ii)$ $\{2, 3\}$ $(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$

$(iii)$ $\{M, A, T, H, E, I, C, S\}$ $(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$

$(iv)$ $\{1, 3, 5, 7, 9\}$ $(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$

Medium

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Write down all the subsets of the following set: $\emptyset $

Easy

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Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\varnothing \subset A$

Easy

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$(i)$ $\{1, 2, 3, 6\}$	$(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$
$(ii)$ $\{2, 3\}$	$(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$
$(iii)$ $\{M, A, T, H, E, I, C, S\}$	$(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$
$(iv)$ $\{1, 3, 5, 7, 9\}$	$(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$

Which of the following pairs of sets are disjoint?$A = \{ x : x \text{ is an even integer} \}$$B = \{ x : x \text{ is an odd integer} \}$

Similar Questions

Write the following set in roster form:$A = \{ x : x \text{ is an integer and } -3 < x < 7 \}$

If a set $A$ has $n$ elements,then the total number of subsets of $A$ is

Write down all the subsets of the following set: $\emptyset $

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?$\varnothing \subset A$

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Which of the following pairs of sets are disjoint?
$A = \{ x : x \text{ is an even integer} \}$
$B = \{ x : x \text{ is an odd integer} \}$

Write the following set in roster form:
$A = \{ x : x \text{ is an integer and } -3 < x < 7 \}$

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\varnothing \subset A$