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ISEE Upper Level Math : How to use a Venn Diagram

研究概念,例子问题&解释for ISEE Upper Level Math

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All ISEE Upper Level Math Resources

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Example Questions

Example Question #1 :Data Analysis

Venn

Refer to the above Venn diagram.

Define universal set $U = \mathbb{N}$ 自然数的集合。

Define setsandas follows:

$A = \left \{ 1,5,9,13,17,21,... \right \}$

$B = \left \{ 2,5,8,11,14,17...\right \}$

Which of the following numbers is an element of the set represented by the gray area in the diagram?

Possible Answers:

102

105

101

104

103

Correct answer:

104

Explanation:

The gray area represents the set of all elements that are inbut not in.

is the set of integers that, when divided by 3, yield remainder 2. Therefore, we can eliminate 102 and 105, both multiples of 3, and 103, which, when divided by 3, yields remainder 1.

is the set of integers that, when divided by 4, yield remainder 1. Since we donotwant an element from this set, we can eliminate 101, but not 104.

104 is the correct choice.

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Example Question #2 :How To Use A Venn Diagram

Venn

In the above Venn diagram, the universal set is defined as $U = \left \{ a, b, c, d, e, f, g, h\right \}$ . Each of the eight letters is placed in its correct region.

What is $A \cap B$ ?

Possible Answers:

$A \cap B = \left \{ b,d,e,g,h \right \}$

$A \cap B = \left \{ a,f \right \}$

$A \cap B = \left \{ a,c,f \right \}$

$A \cap B = \left \{ a,b,d,e,f,g,h \right \}$

$A \cap B = \left \{ b,c,d,e,g,h \right \}$

Correct answer:

$A \cap B = \left \{ a,f \right \}$

Explanation:

$A \cap B$ is the intersection of setsand- that is, the set of all elements ofthat are elements of bothand. We want all of the letters that fall inbothcircles, which from the diagram can be seen to beand. Therefore,

$A \cap B = \left \{ a,f \right \}$

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Example Question #3 :How To Use A Venn Diagram

Venn

In the above Venn diagram, the universal set is defined as $U = \left \{ a, b, c, d, e, f, g, h\right \}$ . Each of the eight letters is placed in its correct region. Which of the following is equal to $\overline{A\cap B}$ ?

Possible Answers:

$\overline{A\cap B} = \left \{ a,f\right \}$

$\overline{A\cap B} = \left \{ b,c,d,e,g,h\right \}$

$\overline{A\cap B} = \left \{ b,d,e,g,h\right \}$

$\overline{A\cap B} = \left \{ c\right \}$

$\overline{A\cap B} = \left \{ a,c,f\right \}$

Correct answer:

$\overline{A\cap B} = \left \{ b,c,d,e,g,h\right \}$

Explanation:

$\overline{A \cap B}$ is the complement of $A \cap B$ - the set of all elements innotin $A \cap B$ .

$A \cap B$ is the intersection of setsand- that is, the set of all elements ofthat are elements of bothand. Therefore, $\overline{A \cap B}$ is the set of all elements that arenotin bothand, which can be seen from the diagram to be all elements exceptand. Therefore,

$\overline{A\cap B} = \left \{ b,c,d,e,g,h\right \}$ .

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Example Question #4 :How To Use A Venn Diagram

Venn

Possible Answers:

$\overline{A\cup B} = \left \{ b,c,d,e,g,h\right \}$

$\overline{A\cup B} = \left \{ a,f\right \}$

$\overline{A\cup B} = \left \{ a,c,f\right \}$

$\overline{A\cup B} = \left \{ c\right \}$

$\overline{A\cup B} = \left \{ b,d,e,g,h\right \}$

Correct answer:

$\overline{A\cup B} = \left \{ c\right \}$

Explanation:

$\overline{A\cup B}$ is the complement of $A\cup B$ - the set of all elements innotin $A\cup B$ .

$A\cup B$ is the union of setsand- the set of all elements in eitheror. Therefore, $\overline{A\cup B}$ is the set of all elements inneithernor, which can be seen from the diagram to be only one element -. Therefore,

$\overline{A\cup B} = \left \{ c\right \}$

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Example Question #5 :How To Use A Venn Diagram

The following Venn diagram depicts the number of students who play hockey, football, and baseball. How many students play football and baseball?

Problem_9

Possible Answers:

Correct answer:

Explanation:

The number of students who play football or baseball can by finding the summer of the number of students who play football alone, baseball alone, baseball and football, and all three sports.

30+20+3+3=56

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Example Question #6 :How To Use A Venn Diagram

A class ofstudents was asked whether they have cats, dogs, or both.The results are depicted in the following Venn diagram. How many students do not have a dog?

Question_5

Possible Answers:

Correct answer:

Explanation:

First, calculate the number of students with a dog:
9+2=11

Next, subtract the number of students with a dog from the total number of students.

30-11=19

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to use a Venn Diagram

研究概念,例子问题&解释for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 :Data Analysis

Example Question #2 :How To Use A Venn Diagram

Example Question #3 :How To Use A Venn Diagram

Example Question #4 :How To Use A Venn Diagram

Example Question #5 :How To Use A Venn Diagram

Example Question #6 :How To Use A Venn Diagram

All ISEE Upper Level Math Resources

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