Question

which of these sets are finite and which of theseare infinite

·The set of lines passing through a point
·The set of lines passing through two given points​

Answer 1

Question :-

1. Which of the following statements are true and which are false? Give reasons for your

(ii) There are an infinite number of lines which pass through two distinct points.

answers.

(1) Only one line can pass through a single point.

(ii) A terminated line can be produced indefinitely on both the sides.

(iv) Iftwo circles are equal, then their radii are equal.

In Fig. 2.9. if AB=PQ and PQ=XY, then AB=XY.

​

Answer :-

(i) False

Reason : If we mark a point O on the surface of a paper. Using pencil and scale, we can draw infinite number of straight lines passing

through O.

(ii) False

Reason : In the following figure, there are many straight lines passing through P. There are many lines, passing through Q. But there is one and only one line which is passing through P as well as Q.

(iii) True

Reason: The postulate 2 says that “A terminated line can be produced indefinitely.”

(iv) True

Reason : Superimposing the region of one circle on the other, we find them coinciding. So, their centres and boundaries coincide.

Thus, their radii will coincide or equal.

(v) True

Reason : According to Euclid’s axiom, things which are equal to the same thing are equal to one another.

Plz mrk as brainliest ❤

Answer 2

The set of lines passing through a point is Infinite.

• In set theory, an infinite set is a set that has no finite set. Infinite sets can be countable or uncountable.

• As we know, an infinite number of lines is capable of passing through a single point.

The set of lines passing through two given points is Finite.

• In mathematics, especially set theory, a finite set is a set that has a finite number of components. In simple words, a finite set is a set in which one could standard count and finish counting.

• As we know that only one line can pass through two given points.

Hence,

The set of lines passing through a point is infinite.

The set of lines passing through two given points is finite.

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