Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is an even natural number} } \dots { x:x \text{ is an integer} }$
${ x:x \text{ is an even natural number} } \dots { x:x \text{ is an integer} }$
(A) Since every even natural number (e.g.,$2, 4, 6, \dots$) is also an integer,the set of even natural numbers is a subset of the set of integers.
Therefore,${ x:x \text{ is an even natural number} } \subset { x:x \text{ is an integer} }$.
Therefore,${ x:x \text{ is an even natural number} } \subset { x:x \text{ is an integer} }$.
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Similar Questions
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
$(i)$ $\{1, 2, 3, 6\}$ $(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$ $(ii)$ $\{2, 3\}$ $(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$ $(iii)$ $\{M, A, T, H, E, I, C, S\}$ $(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$ $(iv)$ $\{1, 3, 5, 7, 9\}$ $(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$
| $(i)$ $\{1, 2, 3, 6\}$ | $(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$ |
| $(ii)$ $\{2, 3\}$ | $(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$ |
| $(iii)$ $\{M, A, T, H, E, I, C, S\}$ | $(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$ |
| $(iv)$ $\{1, 3, 5, 7, 9\}$ | $(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$ |
Medium
View SolutionLet $S = \{0, 1, 5, 4, 7\}$. Then the number of all subsets of $S$ is:
Easy
View SolutionWhich of the following is an example of the null set?
Set of odd natural numbers divisible by $2$.
Set of odd natural numbers divisible by $2$.
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View SolutionList all the elements of the following set:
$E = \{ x : x \text{ is a month of a year not having } 31 \text{ days} \}$
$E = \{ x : x \text{ is a month of a year not having } 31 \text{ days} \}$
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View SolutionExamine whether the following statement is true or false:
$\{x : x \text{ is an even natural number less than } 6\} \subset \{x : x \text{ is a natural number which divides } 36\}$
$\{x : x \text{ is an even natural number less than } 6\} \subset \{x : x \text{ is a natural number which divides } 36\}$
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