Question

State which of the following collections are sets.(i) All even numbers (ii) Stars in the sky(iii) The collection of odd positive integers. 1, 3, 5, …..

Answer 1

Answer:

All these collections are sets.

Step-by-step explanation:

(i) and (iii): The even and odd positive numbers are subsets of the integers (which is a set), then, are sets.

(ii) The stars are discrete, that is, they are "isolated". So we can enumerated them by natural numbers, and, consequently, there is a bijection of some subset of natural numbers with the stars in the sky. In the set theory perspective, sets are preserved by bijections. Then, the collection of stars in the sky is a set.

Answer 2

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DEFINITION

SET : A set is a well defined collection of distinct objects.

EXAMPLE :

• The set of Real numbers
• The set of Natural numbers
• The set of vowels
• The set integers between 1 & 10

FINITE SET : A set is called finite set if it contains finite number of elements

INFINITE SET : A set is called finite set if it contains finite number of elements

TO DETERMINE

State which of the following collections are sets.

(i) All even numbers

(ii) Stars in the sky

(iii) The collection of odd positive integers. 1, 3, 5, …..

CALCULATION

(i) All even numbers

The set is = { 2, 4,6,8,10,.......}

Since it is a well defined collection of objects

So it is a set

In addition it is a infinite set

(ii) Stars in the sky

Since it is a well defined collection of objects

So it is a set

In addition it is a infinite set

(iii) The collection of odd positive integers. 1, 3, 5, …..

Since it is a well defined collection of objects

So it is a set

In addition it is a infinite set

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LEARN MORE FROM BRAINLY

Represent all possible one-one functions from the set A = {1, 2} to the set B = {3,4,5} using arrow diagram.

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