Question

At East Zone University (Ezu) thereare 564 students taking College Algebra or English Comp . 454 are taking college Algebra ,148 are taking English Comp and 38 are taking both College Algebra and English Comp . How many are taking Algebra but Not English Comp?

Answer 1

Step 1: Write the information given in a set notation.

$\begin{gathered} n(U)=564,U\Rightarrow\mleft\lbrace The\text{ entire students}\mright\rbrace \\ E\Rightarrow\mleft\lbrace e\text{nglish comp.}\mright\rbrace \\ C\Rightarrow\mleft\lbrace\text{college algebra}\mright\rbrace \\ \end{gathered}$

Step 2: State the number of students that partake in each subject.

$\begin{gathered} n(C\cap E)=38 \\ n(C\cap E^{\prime})=454-38=416 \\ n(E\cap C^{\prime})=148-38=110 \\ n(C\cup E)^{\prime}=x \end{gathered}$

Step 3: Draw a Venn diagram showing the information above

Step 4: To find the number of students that College Algebra but not English comp., we will check for the number of students that take only College Algebra. This is shown below

$n(C\cap E^{\prime})=416$

Hence, the number of students that are taking Algebra but Not English Comp is 416