In survey of 100 students in the instate of language studies at oxford university the number of students studying various language in the last four years were found to be: Italian 28, german 30, French 42, Italian and german 8, german and French 5, all the three language 3 (A) Venn diagram
(B) how many students were studied all languages
(C) how many students studied only Italy and germany
(D) how many students studied French only
If x studied Italian and French, then
(28+20+42) - (8+5+x) + 3 = 100 - (# not studying any)
Answer
Thanks
Tinaku
To answer the questions related to the survey of students studying different languages at Oxford University, we can use a Venn diagram. A Venn diagram is a diagram that uses circles or overlapping shapes to represent sets of items or concepts. In this case, we can use a Venn diagram to represent the number of students studying each language and the overlap between the languages.
(A) To construct the Venn diagram:
1. Draw a rectangle to represent the total number of students surveyed (100 students).
2. Draw three circles to represent Italian, German, and French. Place them inside the rectangle.
3. Label the circles with the number of students studying each language: Italian (28), German (30), French (42).
4. Determine the overlap by adding numbers given in the survey. Place the appropriate numbers in the overlapping regions. Italian and German (8), German and French (5), all three languages (3).
Now, let's answer the specific questions using the Venn diagram:
(B) To find out how many students studied all three languages:
Look at the region where all three circles overlap, and the number in that overlapping region represents the students studying all languages. Based on the given information, the number of students studying all three languages is 3.
(C) To find out how many students studied only Italian and German:
Add the number of students studying Italian and German together, excluding the overlapping region with French. Based on the given information, the number of students studying only Italian and German is 8.
(D) To find out how many students studied French only:
Subtract the overlapping regions from the total number of students studying French. Based on the given information, the number of students studying French only is 42 - (5 + 3) = 34.
Therefore, the answers to the questions are:
(B) The number of students who studied all languages is 3.
(C) The number of students who studied only Italian and German is 8.
(D) The number of students who studied French only is 34.