Question
(b) In a class of 50 college freshmen.30 are studying c^++ ,25 are studying Java and 10 are studying both languages. by using a venn diagram determine; i.The number of freshmen who are studying either of the computer languages (4 marks) The number of freshmen that are not studying either of the computer , languages 5 (3 marks)
Answer
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(272 Votes)
Llinos
Master · Tutor for 5 years
Answer
1. \(n(C^*+ \cup Java) = 30 + 25 - 10 = 45\)2. \(n(\text{not studying either}) = 50 - 45 = 5\)
Explanation
## Step 1### The formula for the union of two sets is given as: ### \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)Here, \(n(A \cup B)\) is the number of elements in either set A or set B (or both), \(n(A)\) is the number of elements in set A, \(n(B)\) is the number of elements in set B, and \(n(A \cap B)\) is the number of elements common to both sets A and B.## Step 2To find the number of freshmen not studying either of the computer languages, we subtract the number of students studying at least one of the languages from the total number of students in the class.## Step 3Given:- Total number of freshmen \(n(U)\) = 50- Freshmen studying C*+ \(n(C^*+)\) = 30- Freshmen studying Java \(n(Java)\) = 25- Freshmen studying both \(n(C^*+ \cap Java)\) = 10## Step 4Using the formula for the union of two sets:### \(n(C^*+ \cup Java) = n(C^*+) + n(Java) - n(C^*+ \cap Java)\)## Step 5The number of freshmen not studying either of the computer languages is:### \(n(\text{not studying either}) = n(U) - n(C^*+ \cup Java)\)