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Empty Set

State whether...

Question

State whether following set is empty and not?
${x : x$ is a common point to any two parallel lines }

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Solution

Solution:- Empty
Empty set $(ϕ)$ : which has no elements.
Parallel lines do not intersect.
Hence, they have no common point.
Therefore, no element in this set.
Hence, the set of point common to any two parallel lines is empty.

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Similar questions

Which of the following are examples of empty set ?

(i) Set of all even numbers divisible by 5.

(ii) Set of all even prime numbers.

(iii) { $x : x^{2} = 0$ and x is rational}.

(iv) {x : x is a natural number, x < 8 and simultaneously x > 12}.

(v) {x : x is a point common to any two parallel lines}.

5

{x : x^{2} - 2 = 0

x

}

{x : x

x < 8

x > 12

{x : x

}

Find, which of the following sets are empty:

(i)The set of points of intersection of two parallel lines.

(ii) $A = {x : x \in N a n d 5 < x \leq 6}$

(iii) $B = {x : x^{2} + 4 = 0, x \in N}$

(iv) $C = {e v e n n u m b e r s b e t w e e n 6 & 10}$

(v) $D = {p r i m e n u m b e r s b e t w e e n 7 & 11}$

Note : The set, which has no element in it, is called the empty or null set.

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