How to use a Venn Diagram - ISEE Upper Level: Quantitative Reasoning
Card 1 of 64
Let the universal set 
be the set of all positive integers. Define:
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Let the universal set
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Tap to reveal answer
The grayed portion of the Venn diagram corresponds to those integers which are not in any of 
, 
, or 
. Therefore, we eliminate any choices that are in any of the three sets.
is the set of integers which end in 1 or 6; we can eliminate 166 and 176 immediately.
is the set of perfect square integers; we can eliminate 144, since 
.
is the set of integers which, when divided by 4, yields remainder 2. Since 
, we can eliminate 154.
All four choices have been eliminated.
The grayed portion of the Venn diagram corresponds to those integers which are not in any of
All four choices have been eliminated.
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In the above Venn diagram, the universal set is defined as 
. Each of the eight letters is placed in its correct region. Which of the following is equal to 
?
In the above Venn diagram, the universal set is defined as
Tap to reveal answer
is the complement of 
- the set of all elements in 
not in 
.
is the union of sets 
and 
- the set of all elements in either 
or 
. Therefore, 
is the set of all elements in neither 
nor 
, which can be seen from the diagram to be only one element - 
. Therefore,
← Didn't Know|Knew It →
Let the universal set be the set of all positive integers. Define:
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Let the universal set
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Tap to reveal answer
The grayed portion of the Venn diagram corresponds to those integers which are not in any of , , or . Therefore, we eliminate any choices that are in any of the three sets.
is the set of integers which end in 1 or 6; we can eliminate 166 and 176 immediately.
is the set of perfect square integers; we can eliminate 144, since .
is the set of integers which, when divided by 4, yields remainder 2. Since , we can eliminate 154.
All four choices have been eliminated.
The grayed portion of the Venn diagram corresponds to those integers which are not in any of
All four choices have been eliminated.
← Didn't Know|Knew It →
Refer to the above Venn diagram.
Define universal set 
, the set of natural numbers.
Define sets 
and 
as follows:
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Refer to the above Venn diagram.
Define universal set
Define sets
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Tap to reveal answer
The gray area represents the set of all elements that are in 
but 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 do not want an element from this set, we can eliminate 101, but not 104.
104 is the correct choice.
The gray area represents the set of all elements that are in
104 is the correct choice.
← Didn't Know|Knew It →
Let the universal set be the set of all positive integers. Define:
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Let the universal set
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Tap to reveal answer
The grayed portion of the Venn diagram corresponds to those integers which are not in any of , , or . Therefore, we eliminate any choices that are in any of the three sets.
is the set of integers which end in 1 or 6; we can eliminate 166 and 176 immediately.
is the set of perfect square integers; we can eliminate 144, since .
is the set of integers which, when divided by 4, yields remainder 2. Since , we can eliminate 154.
All four choices have been eliminated.
The grayed portion of the Venn diagram corresponds to those integers which are not in any of
All four choices have been eliminated.
← Didn't Know|Knew It →
Refer to the above Venn diagram.
Define universal set , the set of natural numbers.
Define sets and as follows:
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Refer to the above Venn diagram.
Define universal set
Define sets
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Tap to reveal answer
The gray area represents the set of all elements that are in but 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 do not want an element from this set, we can eliminate 101, but not 104.
104 is the correct choice.
The gray area represents the set of all elements that are in
104 is the correct choice.
← Didn't Know|Knew It →
Refer to the above Venn diagram.
Define universal set , the set of natural numbers.
Define sets and as follows:
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Refer to the above Venn diagram.
Define universal set
Define sets
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Tap to reveal answer
The gray area represents the set of all elements that are in but 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 do not want an element from this set, we can eliminate 101, but not 104.
104 is the correct choice.
The gray area represents the set of all elements that are in
104 is the correct choice.
← Didn't Know|Knew It →
Let the universal set be the set of all positive integers. Define:
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Let the universal set
Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?
Tap to reveal answer
The grayed portion of the Venn diagram corresponds to those integers which are not in any of , , or . Therefore, we eliminate any choices that are in any of the three sets.
is the set of integers which end in 1 or 6; we can eliminate 166 and 176 immediately.
is the set of perfect square integers; we can eliminate 144, since .
is the set of integers which, when divided by 4, yields remainder 2. Since , we can eliminate 154.
All four choices have been eliminated.
The grayed portion of the Venn diagram corresponds to those integers which are not in any of
All four choices have been eliminated.
← Didn't Know|Knew It →
Refer to the above Venn diagram.
Define universal set , the set of natural numbers.
Define sets and as follows:
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Refer to the above Venn diagram.
Define universal set
Define sets
Which of the following numbers is an element of the set represented by the gray area in the diagram?
Tap to reveal answer
The gray area represents the set of all elements that are in but 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 do not want an element from this set, we can eliminate 101, but not 104.
104 is the correct choice.
The gray area represents the set of all elements that are in
104 is the correct choice.
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region. Which of the following is equal to ?
In the above Venn diagram, the universal set is defined as
Tap to reveal answer
is the complement of - the set of all elements in not in .
is the union of sets and - the set of all elements in either or . Therefore, is the set of all elements in neither nor , which can be seen from the diagram to be only one element - . Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as 
. Each of the eight letters is placed in its correct region.
What is 
?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the union of sets 
and 
- that is, the set of all elements of 
that are elements of either 
or 
. We want all of the letters that fall in either circle, which from the diagram can be seen to be all of the letters except 
. Therefore,
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In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region.
What is ?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the union of sets and - that is, the set of all elements of that are elements of either or . We want all of the letters that fall in either circle, which from the diagram can be seen to be all of the letters except . Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as 
. Each of the eight letters is placed in its correct region.
What is 
?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the intersection of sets 
and 
- that is, the set of all elements of 
that are elements of both 
and 
. We want all of the letters that fall in both circles, which from the diagram can be seen to be 
and 
. Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as 
. Each of the eight letters is placed in its correct region. Which of the following is equal to 
?
In the above Venn diagram, the universal set is defined as
Tap to reveal answer
is the complement of 
- the set of all elements in 
not in 
.
is the intersection of sets 
and 
- that is, the set of all elements of 
that are elements of both 
and 
. Therefore, 
is the set of all elements that are not in both 
and 
, which can be seen from the diagram to be all elements except 
and 
. Therefore,
.
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region.
What is ?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the union of sets and - that is, the set of all elements of that are elements of either or . We want all of the letters that fall in either circle, which from the diagram can be seen to be all of the letters except . Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region.
What is ?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the intersection of sets and - that is, the set of all elements of that are elements of both and . We want all of the letters that fall in both circles, which from the diagram can be seen to be and . Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region. Which of the following is equal to ?
In the above Venn diagram, the universal set is defined as
Tap to reveal answer
is the complement of - the set of all elements in not in .
is the intersection of sets and - that is, the set of all elements of that are elements of both and . Therefore, is the set of all elements that are not in both and , which can be seen from the diagram to be all elements except and . Therefore,
.
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region.
What is ?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the union of sets and - that is, the set of all elements of that are elements of either or . We want all of the letters that fall in either circle, which from the diagram can be seen to be all of the letters except . Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region.
What is ?
In the above Venn diagram, the universal set is defined as
What is
Tap to reveal answer
is the intersection of sets and - that is, the set of all elements of that are elements of both and . We want all of the letters that fall in both circles, which from the diagram can be seen to be and . Therefore,
← Didn't Know|Knew It →
In the above Venn diagram, the universal set is defined as . Each of the eight letters is placed in its correct region. Which of the following is equal to ?
In the above Venn diagram, the universal set is defined as
Tap to reveal answer
is the complement of - the set of all elements in not in .
is the intersection of sets and - that is, the set of all elements of that are elements of both and . Therefore, is the set of all elements that are not in both and , which can be seen from the diagram to be all elements except and . Therefore,
.
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