In the class of 20 pupils there are 12 pupils who study English but not history,4 pupils who study history but not English and 1 who studies neither not history.How many pupils in the class study history to solve this equation
solve what equation?
and "neither not history" is just gibberish.
Did you draw a Venn diagram?
since 20-1 = 19 students study something,
19 - (12+4) = 3 study both subjects.
So 4+3 = 7 study History
To solve this equation, let's use a Venn diagram to represent the information given.
Let's label three circles: one for English, one for History, and one for Neither English nor History. We know that there are 12 pupils who study English but not History, 4 pupils who study History but not English, and 1 pupil who studies neither.
First, let's fill in the information we have:
English: 12
History: 4
Neither English nor History: 1
Next, we can calculate the number of pupils who study both English and History. To do this, we subtract the number of pupils who study English only (12) from the total number of pupils who study English (12) since the difference between these two groups would be the ones who study both:
English only: 12
English: 12
Both English and History: 12 - 12 = 0
Now we can calculate the number of pupils who study History. This includes those who study History only (4) and those who study both English and History (0):
History only: 4
Both English and History: 0
Total number of pupils studying History: 4 + 0 = 4.
Therefore, in the class of 20 pupils, 4 pupils study History.
To solve this equation, we need to use the principle of inclusion-exclusion, which states that:
Total = English + History - (English and History) + Neither
Let's break down the information given:
English = 12 (pupils who study English but not history)
History = ?
English and History = ?
Neither = 1 (pupil who studies neither English nor history)
We know that the class has a total of 20 pupils, so let's substitute the values into the equation:
20 = 12 + History - (English and History) + 1
Now we need to determine the value of (English and History). To find this, we can subtract the number of pupils who study English but not history from the total number of pupils who study English:
(English and History) = English - (English but not History)
(English and History) = 12 - 4 (pupils who study history but not English)
(English and History) = 8
Now, let's go back to the equation and plug in this value:
20 = 12 + History - 8 + 1
Next, simplify the equation:
20 = 5 + History
Finally, isolate the variable (History):
History = 20 - 5
History = 15
Therefore, there are 15 pupils in the class who study history.