For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?
For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?
- [KVPY 2013]
- A
$S_n$ has a multiple of $19$
- B
$S_n$ has a prime
- C
$S_n$ has at least four multiples of $5$
- D
$S_n$ has at most six primes
Similar Questions
Write the set $\{ x:x$ is a positive integer and ${x^2} < 40\} $ in the roster form.
Write the set $\{ x:x$ is a positive integer and ${x^2} < 40\} $ in the roster form.
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
$(i)$ $\{1,2,3,6\}$
$(a)$ $\{ x:x$ is a prime number and a divisor $6\} $
$(ii)$ $\{2,3\}$
$(b)$ $\{ x:x$ is an odd natural number less than $10\} $
$(iii)$ $\{ M , A , T , H , E , I , C , S \}$
$(c)$ $\{ x:x$ is natural number and divisor of $6\} $
$(iv)$ $\{1,3,5,7,9\}$
$(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
| $(i)$ $\{1,2,3,6\}$ | $(a)$ $\{ x:x$ is a prime number and a divisor $6\} $ |
| $(ii)$ $\{2,3\}$ | $(b)$ $\{ x:x$ is an odd natural number less than $10\} $ |
| $(iii)$ $\{ M , A , T , H , E , I , C , S \}$ | $(c)$ $\{ x:x$ is natural number and divisor of $6\} $ |
| $(iv)$ $\{1,3,5,7,9\}$ | $(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $ |
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The set of animals living on the earth
State whether each of the following set is finite or infinite :
The set of animals living on the earth
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$\{1,2,5\}\subset A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,5\}\subset A$
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List all the subsets of the set $\{-1,0,1\}.$