CA Foundation Exam > CA Foundation Questions > If A = { 1, 2, 3, 5, 7} and B = {1, 3, 6, 10,...
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If A = { 1, 2, 3, 5, 7} and B = {1, 3, 6, 10, 15}. Cardinal number of A~B is
- a)3
- b)4
- c)6
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If A = { 1, 2, 3, 5, 7} and B = {1, 3, 6, 10, 15}. Cardinal number of ...
Cardinal Number of A~B
Definition of Cardinal Number
Cardinal number is a number that represents the size or quantity of a set.
Given Sets
A = { 1, 2, 3, 5, 7}
B = {1, 3, 6, 10, 15}
Definition of A~B
A~B represents the symmetric difference of A and B, which is the set of elements that are in either A or B, but not in both.
Calculation of Cardinal Number of A~B
To calculate the cardinal number of A~B, we need to find the elements that are in either A or B, but not in both.
1. Elements in A but not in B
{2, 5, 7}
2. Elements in B but not in A
{6, 10, 15}
3. Elements in both A and B
{1, 3}
4. Elements in either A or B, but not in both
{2, 5, 7, 6, 10, 15}
5. Cardinal number of A~B
The cardinal number of A~B is the number of elements in the set {2, 5, 7, 6, 10, 15}, which is 3.
Therefore, the correct answer is option A, 3.
Definition of Cardinal Number
Cardinal number is a number that represents the size or quantity of a set.
Given Sets
A = { 1, 2, 3, 5, 7}
B = {1, 3, 6, 10, 15}
Definition of A~B
A~B represents the symmetric difference of A and B, which is the set of elements that are in either A or B, but not in both.
Calculation of Cardinal Number of A~B
To calculate the cardinal number of A~B, we need to find the elements that are in either A or B, but not in both.
1. Elements in A but not in B
{2, 5, 7}
2. Elements in B but not in A
{6, 10, 15}
3. Elements in both A and B
{1, 3}
4. Elements in either A or B, but not in both
{2, 5, 7, 6, 10, 15}
5. Cardinal number of A~B
The cardinal number of A~B is the number of elements in the set {2, 5, 7, 6, 10, 15}, which is 3.
Therefore, the correct answer is option A, 3.
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Community Answer
If A = { 1, 2, 3, 5, 7} and B = {1, 3, 6, 10, 15}. Cardinal number of ...
A={1,2,3,5,7}
B={1,3,6,10,15}
A-B = A-(A intersection B)
(A intersection B) means common digits in A &B i.e. here 1&3
=1,2,3,5,7 -1,3
=2,5,7. (total digits=3
Hence ans is 3.
B={1,3,6,10,15}
A-B = A-(A intersection B)
(A intersection B) means common digits in A &B i.e. here 1&3
=1,2,3,5,7 -1,3
=2,5,7. (total digits=3
Hence ans is 3.
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If A = { 1, 2, 3, 5, 7} and B = {1, 3, 6, 10, 15}. Cardinal number of A~B isa)3b)4c)6d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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