(A) null set (or empty set) is a set that contains no elements.For the set of odd natural numbers divisible by $2$:An odd number is of the form $2n +

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${x : x \text{ is an odd natural number and } x \text{ is divisible by } 2}$

(A) null set (or empty set) is a set that contains no elements.For the set of odd natural numbers divisible by $2$:An odd number is of the form $2n + 1$,where $n$ is an integer.By definition,an odd number is not divisible by $2$.Therefore,there are no odd natural numbers divisible by $2$.Thus,the set is a null set (denoted by $\emptyset$ or $\{\}$).

Class 11 Mathematics Set Theory Basic of Set theory

Easy

Which of the following is an example of the null set?
Set of odd natural numbers divisible by $2$.

A
${x : x \text{ is an odd natural number and } x \text{ is divisible by } 2}$
B
${x : x \text{ is an even prime number}}$
C
${x : x \text{ is a natural number, } x < 5 \text{ and } x > 7}$
D
${x : x \text{ is a point common to any two parallel lines}}$

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Basic of Set theory

Write the following set in the set-builder form: $\{ 1, 4, 9, \ldots, 100 \}$

Easy

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Which of the following is an example of the null set?
$\{ y : y \text{ is a point common to any two parallel lines} \}$

Easy

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

Easy

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Examine whether the following statement is true or false:
$\{a\} \subset \{a, b, c\}$

Easy

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Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)

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Which of the following is an example of the null set?Set of odd natural numbers divisible by $2$.

Similar Questions

Write the following set in the set-builder form: $\{ 1, 4, 9, \ldots, 100 \}$

Which of the following is an example of the null set?$\{ y : y \text{ is a point common to any two parallel lines} \}$

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

Examine whether the following statement is true or false:$\{a\} \subset \{a, b, c\}$

Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)

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Which of the following is an example of the null set?
Set of odd natural numbers divisible by $2$.

Which of the following is an example of the null set?
$\{ y : y \text{ is a point common to any two parallel lines} \}$

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

Examine whether the following statement is true or false:
$\{a\} \subset \{a, b, c\}$