# Let $U$ be the set of all people and $M$ = {Males}, $S$ = {college students}, $T$= {teenagers},$W$ =

{people having heights more than five feet}. Express each of the following in the notation of set theory.

(i) College people having heights more than five feet.

(ii) People who are not teenagers and have their heights less than five feet.

(iii) All people who are neither males nor teenagers nor college students.

Last updated date: 01st Apr 2023

•

Total views: 311.4k

•

Views today: 3.88k

Answer

Verified

311.4k+ views

Hint: - The following can be done by set theory as well as by creating charts but using set theory is quite a simpler way to solve.

(i) College people having heights more than five feet. These boys should belong to

both $S$ and $W$ as they have to satisfy both the properties.

$\therefore S \cap W$

(ii) People who are not teenagers and have their heights less than five feet. Teenagers belong

To $T$. Those who are not teenagers belong to $T'$. Similarly $W'$ and hence

$T' \cap W' = {\left\{ {T \cup W} \right\}^\prime }$

(iii) All people who are neither males nor teenagers nor college students

$M' \cap T' \cap S' = {\left\{ {M \cup T \cup S} \right\}^\prime }$

Note: - The signs used above are signs of set theory, where $ \cup $ represents union of two sets, $ \cap

$ represents the intersection of two sets and a bar like sign on the top of any letter represents the

conjugate of the set. (Like this:$A'$ )

(i) College people having heights more than five feet. These boys should belong to

both $S$ and $W$ as they have to satisfy both the properties.

$\therefore S \cap W$

(ii) People who are not teenagers and have their heights less than five feet. Teenagers belong

To $T$. Those who are not teenagers belong to $T'$. Similarly $W'$ and hence

$T' \cap W' = {\left\{ {T \cup W} \right\}^\prime }$

(iii) All people who are neither males nor teenagers nor college students

$M' \cap T' \cap S' = {\left\{ {M \cup T \cup S} \right\}^\prime }$

Note: - The signs used above are signs of set theory, where $ \cup $ represents union of two sets, $ \cap

$ represents the intersection of two sets and a bar like sign on the top of any letter represents the

conjugate of the set. (Like this:$A'$ )

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE