In a college, there are 300 students. 140 like coffee, 80 like both tea and coffee, with the aid of a big…

Question

In a college, there are 300 students. 140 like coffee, 80 like both tea and coffee, with the aid of a big diagram. How many students like tea only? How many students like coffee? How many students like tea? How many students like at least one? How many students like neither tea nor coffee?

ScanSolve AI Tutor · Accepted Answer

Hapa kuna masuluhisho kwa maswali yako:

Tunapewa taarifa zifuatazo:

Jumla ya wanafunzi $|U| = 200$
Wanafunzi wanaopenda chai $|T| = 140$
Wanafunzi wanaopenda kahawa $|C| = 130$
Wanafunzi wanaopenda chai na kahawa zote mbili $|T \cap C| = 80$

A) Wanafunzi wangapi wanapenda chai pekee?

Ili kupata wanafunzi wanaopenda chai pekee, tunatoa idadi ya wanafunzi wanaopenda chai na kahawa kutoka kwa idadi ya wanafunzi wanaopenda chai.
$|T \text{ pekee}| = |T| - |T \cap C|$ $|T \text{ pekee}| = 140 - 80$ $|T \text{ pekee}| = 60$
Wanafunzi wanaopenda chai pekee ni $\boxed{\text{60}}$ .

B) Wanafunzi wangapi wanapenda kahawa pekee?
Ili kupata wanafunzi wanaopenda kahawa pekee, tunatoa idadi ya wanafunzi wanaopenda chai na kahawa kutoka kwa idadi ya wanafunzi wanaopenda kahawa.
$|C \text{ pekee}| = |C| - |T \cap C|$ $|C \text{ pekee}| = 130 - 80$ $|C \text{ pekee}| = 50$
Wanafunzi wanaopenda kahawa pekee ni $\boxed{\text{50}}$ .

D) Wanafunzi wangapi wanapenda angalau kimoja kati ya chai au kahawa?
Idadi ya wanafunzi wanaopenda angalau kimoja (chai au kahawa au zote mbili) inapatikana kwa kutumia kanuni ya muungano wa seti.
$|T \cup C| = |T| + |C| - |T \cap C|$ $|T \cup C| = 140 + 130 - 80$ $|T \cup C| = 270 - 80$ $|T \cup C| = 190$
Wanafunzi wanaopenda angalau kimoja ni $\boxed{\text{190}}$ .

C) Wanafunzi wangapi hawapendi chai wala kahawa?
Ili kupata wanafunzi ambao hawapendi chai wala kahawa, tunatoa idadi ya wanafunzi wanaopenda angalau kimoja kutoka kwa jumla ya wanafunzi.
$|\text{Wala hawapendi}| = |U| - |T \cup C|$ $|\text{Wala hawapendi}| = 200 - 190$ $|\text{Wala hawapendi}| = 10$
Wanafunzi ambao hawapendi chai wala kahawa ni $\boxed{\text{10}}$ .

In a college, there are 300 students. 140 like coffee, 80 like both tea and coffee, with the aid of a big diagram. How many students like tea only? How many students like coffee? How many students like tea? How many students like at least one? How many students like neither tea nor coffee?

Step-by-step solution

Ili kupata wanafunzi wanaopenda chai pekee, tunatoa idadi ya wanafunzi wanaopenda chai na kahawa kutoka kwa idadi ya wanafunzi wanaopenda chai.

Ili kupata wanafunzi wanaopenda kahawa pekee, tunatoa idadi ya wanafunzi wanaopenda chai na kahawa kutoka kwa idadi ya wanafunzi wanaopenda kahawa.

Idadi ya wanafunzi wanaopenda angalau kimoja (chai au kahawa au zote mbili) inapatikana kwa kutumia kanuni ya muungano wa seti.

Ili kupata wanafunzi ambao hawapendi chai wala kahawa, tunatoa idadi ya wanafunzi wanaopenda angalau kimoja kutoka kwa jumla ya wanafunzi.

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