Question

A) A = {prime numbers}, B = ?

b) B = {letters of the word 'elephant'}, C = ?
c) C = {x: x is an odd number less than 5}, D = ?
d) D = {y: y is a factor of 12}, A = ?
a) Set is a collection of distinct elements. Example: A = {1, 2, 3}
b) Yes, the collection of nice Nepali songs is a set because it is a well-defined collection.
c) Three methods are listing method (e.g., A = {1, 2, 3}), set-builder notation (e.g., B = x ), and roster method (e.g., C = {1, 3, 5}).
d) In set-builder method, we write a set as x . Example: D = y

Answer 1

This question pertains to mathematical sets and probabilities, focusing on the intersection and union of sets and the concept of mutually exclusive events. Example operations with sets A and B are provided, as well as an explanation of their mutual exclusivity with set C.

Step-by-step explanation:

The question is focused on the concept of sets and probability within the field of mathematics. Specifically, it deals with the operations involved in sets such as the intersection (AND) and the union (OR) of two sets, and establishes the probability of an event occurring within a sample space. Additionally, the discussion touches on mutually exclusive events and concepts related to set notation.

Notably, intersection (A AND B) refers to elements that are common to both sets A and B. For example, if A represents even numbers and B represents numbers greater than 13, A AND B would contain the set of numbers {14,16,18}. On the other hand, the union (A OR B) consists of all elements that are in either set A, set B, or both, without duplicates. Therefore, A OR B for the given sets would be {2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19}.

The concept of mutual exclusivity also comes into play, indicating that two events have no common outcomes, as exemplified by A and C being mutually exclusive with a probability of 0.