Question:

Consider A={1,2}A = \{1, 2\} and B={2,3}B = \{2, 3\} then which of the following options is correct?

Updated On: Jul 6, 2022
  • P(A∪B)≠P(A)∪P(B)P\left(A \cup B\right) \ne P\left(A\right) \cup P\left(B\right)
  • P(A∪B)=P(A)∪P(B)P\left(A \cup B\right) = P\left(A\right) \cup P\left(B\right)
  • P(A∪B)≠P(A)∩P(B)P\left(A \cup B\right) \ne P\left(A\right) \cap P\left(B\right)
  • None of these
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The Correct Option is A

Solution and Explanation

Here P(A)={ϕ,{1},{2},{1,2}}P\left(A\right) = \left\{\phi, \left\{1\right\}, \left\{2\right\}, \left\{1, 2\right\}\right\}, P(B)={ϕ,{2},{3},{2,3}}P\left(B\right) = \left\{\phi, \left\{2\right\}, \left\{3\right\}, \left\{2, 3\right\}\right\} A∪B={1,2,3}A \cup B = \left\{1, 2, 3\right\} ∴P(A∪B)={ϕ,{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3}}\therefore P\left(A \cup B\right) = \left\{\phi, \left\{1\right\}, \left\{2\right\}, \left\{3\right\}, \left\{1, 2\right\}, \left\{2, 3\right\}, \left\{1, 3\right\}, \left\{1, 2, 3\right\}\right\} P(A)∪P(B)={ϕ,{1},{2},{3},{1,2},{2,3}}P\left(A\right) \cup P\left(B\right) = \left\{\phi, \left\{1\right\}, \left\{2\right\}, \left\{3\right\}, \left\{1, 2\right\}, \left\{2, 3\right\}\right\} ∴P(A∪B)≠P(A)∪P(B)\therefore P\left(A \cup B\right) \ne P\left(A\right) \cup P\left(B\right)
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Notes on Sets

Concepts Used:

Sets

Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.

Example of set: Set of vowels A={a,e,i,o,u}

Representation of Sets

There are three basic notation or representation of sets are as follows:

Statement Form: The statement representation describes a statement to show what are the elements of a set.

  • For example, Set A is the list of the first five odd numbers.

Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.

  • For example represent the set of vowels in roster form.

A={a,e,i,o,u}

Set Builder Form: 

  1. The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
  2. The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
  3. For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
  4. Sometimes a ":" is used in the place of the "|".