Write the set $\{ \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7} \}$ in the set-builder form.
- A$\{ x : x = \frac{n}{n+1}, n \in \mathbb{N}, 1 \le n \le 6 \}$
- B$\{ x : x = \frac{n}{n+1}, n \in \mathbb{N}, 1 \le n < 6 \}$
- C$\{ x : x = \frac{n}{n+1}, n \in \mathbb{N}, 1 < n \le 6 \}$
- D$\{ x : x = \frac{n}{n-1}, n \in \mathbb{N}, 1 \le n \le 6 \}$
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In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:
Medium
View SolutionMatch each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
$(i) \{ P,R,I,N,C,A,L\} $ $(a) \{ x:x \text{ is a positive integer and is a divisor of } 18\} $ $(ii) \{ 0\} $ $(b) \{ x:x \text{ is an integer and } x^2 - 9 = 0\} $ $(iii) \{ 1,2,3,6,9,18\} $ $(c) \{ x:x \text{ is an integer and } x + 1 = 1\} $ $(iv) \{ 3, -3\} $ $(d) \{ x:x \text{ is a letter of the word } PRINCIPAL\} $
| $(i) \{ P,R,I,N,C,A,L\} $ | $(a) \{ x:x \text{ is a positive integer and is a divisor of } 18\} $ |
| $(ii) \{ 0\} $ | $(b) \{ x:x \text{ is an integer and } x^2 - 9 = 0\} $ |
| $(iii) \{ 1,2,3,6,9,18\} $ | $(c) \{ x:x \text{ is an integer and } x + 1 = 1\} $ |
| $(iv) \{ 3, -3\} $ | $(d) \{ x:x \text{ is a letter of the word } PRINCIPAL\} $ |
Medium
View SolutionWrite the solution set of the equation $x^2 + x - 2 = 0$ in roster form.
Easy
View SolutionConsider the experiment of rolling a die. Let $A$ be the event 'getting a prime number' and $B$ be the event 'getting an odd number'. Write the sets representing the events $A$ and $B$.
Easy
View SolutionIn set-builder form,the empty set is represented by
Easy
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