thank you! There are a total of 136 foreign language students in a high school w

Question

thank you!

There are a total of 136 foreign language students in a high school where they offer Spanish, French, and German. There are 13 students who take French and German, 22 students who take French Spanish, 12 students who take German and Spanish, and 2 students who take all three languages. If there are 64 Spanish students, 65 French students, and 52 German students, find: How many students take French only. How many students take French AND German but not Spanish. How many students take French OR German but not Spanish.

Explanation / Answer

Here let F is the set of French students, G is the set of German students and S is the set of spanish students, so it is given that

universal set n(U)= 136, n(F and G) =13, n(F and S) = 22    , n(G and S)= 12 , n(S)= 64, n(F)= 65 and n(G) = 52

n(F and G and S )= 2

then n(F only )= n(F) -[n(F and G) + n(F and S )- n( F and G and S)]

=65 -(13 +22 - 2) = 65 - (35-2 )= 65- 33 = 32

so there are total 32 students who speak freach only. This is the answer of part a)

=================================================================================

Again n(F and G but not S)= n( F and G)- n(F and G and S)

=13-2= 11

This is the answer of part b)

================================================================================

n(F or G but not S) = n(F only) + n(G only) +n(F and G but not S)

Now n(G only ) = n(G)-[n(S and G)+n(F and G) -n(F and G and S)]

=52 -(12 +13-2) = 52-23 = 29

So by above formula,

n(F or G but not S ) = 32+ 29 +11

=72

This is the answer of part c.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.