math problem,Venn diagram please helppp me
Answers
Answer- The above question is from the chapter 'Sets'.
Let's know about sets first.
Sets: Collection of well-defined objects is called a set.
- Natural numbers: Counting numbers i.e. 1, 2, 3, 4, ... are called natural numbers. Set of natural numbers is denoted by N.
- Whole numbers: 0 and all natural numbers are called whole numbers. Set of whole numbers is denoted by W.
- Integers: Negatives of natural numbers, 0 and all positive natural numbers are called integers. Set of integers is denoted by Z.
- Rational numbers: Numbers which can be written in the form of p/q where p, q are integers and q ≠ 0 are called rational numbers. Set of rational numbers is denoted by Q.
- Irrational numbers: Numbers which can't be written in the form of p/q where p, q are integers are called irrational numbers. Set of irrational numbers is denoted by T.
- Real Numbers: Collection of rational and irrational numbers is called real numbers. Set of real numbers is denoted by R.
Venn Diagram: A venn diagram, named after a logician called John Venn, is a logical diagram used to represent sets and the relationships between them.
Universal Set: It is the set which contains all the existing elements.
It is denoted by U.
Union of sets: For two sets A and B, union of A and B is that set which contains all the elements of A and B.
Symbol: ∪
Intersection of sets: For two sets A and B, intersection of A and B is that set which contains the common elements of A and B.
Symbol: ∩
Difference of sets: For two sets A and B, A - B is the set which contains elements of set A and not B.
Symbol: -
n(A): Number of elements in a set A is denoted by n(A).
Important formula: n(A∩B) = n(A) + n(B) - n(A∪B)
Given question: Do the following. Represent the sets and draw a Venn diagram.
Among the 70 residents in Barangay General P. Santos, 53 like eating in Restaurant A while 42 like eating in Restaurant B. How many like eating in both restaurant A and B? In restaurant A only? In restaurant B only?
Solution: n(A) = 53 = No. of people who like eating in Restaurant A
n(B) = 42 = No. of people who like eating in Restaurant B
n(A∪B) = 70 = Total no. of residents
n(A∩B) = No. of people who like eating in both Restaurants A and B
n(A∩B) = n(A) + n(B) - n(A∪B)
n(A∩B) = 53 + 42 - 70
n(A∩B) = 95 - 70
n(A∩B) = 25 (Represented by Red region)
No. of people who like to eat in Restaurant A only = A - B
No. of people who like to eat in Restaurant A only = 53 - 25
No. of people who like to eat in Restaurant A = 28 (Represented by Green region)
No. of people who like to eat in Restaurant B only = B - A
No. of people who like to eat in Restaurant B only = 42 - 25
No. of people who like to eat in Restaurant B = 17 (Represented by Blue Region)
(Diagram has been attached.)
Answer:
Answer- The above question is from the chapter 'Sets'.
Let's know about sets first.
Sets: Collection of well-defined objects is called a set.
Natural numbers: Counting numbers i.e. 1, 2, 3, 4, ... are called natural numbers. Set of natural numbers is denoted by N.
Whole numbers: 0 and all natural numbers are called whole numbers. Set of whole numbers is denoted by W.
Integers: Negatives of natural numbers, 0 and all positive natural numbers are called integers. Set of integers is denoted by Z.
Rational numbers: Numbers which can be written in the form of p/q where p, q are integers and q ≠ 0 are called rational numbers. Set of rational numbers is denoted by Q.
Irrational numbers: Numbers which can't be written in the form of p/q where p, q are integers are called irrational numbers. Set of irrational numbers is denoted by T.
Real Numbers: Collection of rational and irrational numbers is called real numbers. Set of real numbers is denoted by R.
Venn Diagram: A venn diagram, named after a logician called John Venn, is a logical diagram used to represent sets and the relationships between them.
Universal Set: It is the set which contains all the existing elements.
It is denoted by U.
Union of sets: For two sets A and B, union of A and B is that set which contains all the elements of A and B.
Symbol: ∪
Intersection of sets: For two sets A and B, intersection of A and B is that set which contains the common elements of A and B.
Symbol: ∩
Difference of sets: For two sets A and B, A - B is the set which contains elements of set A and not B.
Symbol: -
n(A): Number of elements in a set A is denoted by n(A).
Important formula: n(A∩B) = n(A) + n(B) - n(A∪B)
Given question: Do the following. Represent the sets and draw a Venn diagram.
Among the 70 residents in Barangay General P. Santos, 53 like eating in Restaurant A while 42 like eating in Restaurant B. How many like eating in both restaurant A and B? In restaurant A only? In restaurant B only?
Solution: n(A) = 53 = No. of people who like eating in Restaurant A
n(B) = 42 = No. of people who like eating in Restaurant B
n(A∪B) = 70 = Total no. of residents
n(A∩B) = No. of people who like eating in both Restaurants A and B
n(A∩B) = n(A) + n(B) - n(A∪B)
n(A∩B) = 53 + 42 - 70
n(A∩B) = 95 - 70
n(A∩B) = 25 (Represented by Red region)
No. of people who like to eat in Restaurant A only = A - B
No. of people who like to eat in Restaurant A only = 53 - 25
No. of people who like to eat in Restaurant A = 28 (Represented by Green region)
No. of people who like to eat in Restaurant B only = B - A
No. of people who like to eat in Restaurant B only = 42 - 25
No. of people who like to eat in Restaurant B = 17 (Represented by Blue Region)
(Diagram has been attached.)
