Question

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.

Answer 1

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 $T^{\prime }$. Similarly $W^{\prime }$ and hence
$T^{\prime }\cap W^{\prime }={\left\{T\cup W\right\}}^{\prime }$
(iii) All people who are neither males nor teenagers nor college students
$M^{\prime }\cap T^{\prime }\cap S^{\prime }={\left\{M\cup T\cup S\right\}}^{\prime }$

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:$A^{\prime }$ )