Question

If A=(5, 6,7)B=(6,7,8,9) find A-(A-B) and A intersection B. What is your observation
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Answer 1

Given that two sets are there:

A = {5, 6, 7}

B = {6, 7, 8, 9}

To find: A - (A - B) = ?

A $\cap$ B = ?

Solution: First of all, let us have a look at the definition of Minus and Intersection in sets.

1. Minus of two sets: Minus of two sets is a set that contains the elements of first set that are not present in the second set.

For example:

P = {2, 3}

Q = {3, 4}

P - Q = {2}

2. Intersection of two sets: The intersection of two sets is a set that contains the elements that are common in both the sets.

P = {2, 3}

Q = {3, 4}

P $\cap$ Q = {3}

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Now, applying both the definitions to find out the answers of given question.

A - (A - B) = ?

A - B is the set that will contain all the elements of A that are not present in set B.

So, A - B = {5}

Now, A - (A - B)  will be the set that will contain all the elements of A that are not present in set A - B.

A - (A - B) = {6, 7}

A $\cap$ B will contain the elements that are present in both the sets A and B.

A $\cap$ B = {6, 7}

By looking at the answers above, we observe that both the sets are equal to each other i.e.

A - (A - B) =  A $\cap$ B = {6,7}

Answer 2

Answer:

hello friend ! here is your answer !

Step-by-step explanation:

Solution: First of all, let us have a look at the definition of Minus and Intersection in sets.

1. Minus of two sets: Minus of two sets is a set that contains the elements of first set that are not present in the second set.

For example:

P = {2, 3}

Q = {3, 4}

P - Q = {2}

2. Intersection of two sets: The intersection of two sets is a set that contains the elements that are common in both the sets.

P = {2, 3}

Q = {3, 4}

P \cap∩ Q =3

Now, applying both the definitions to find out the answers of given question.

A - (A - B) = ?

A - B is the set that will contain all the elements of A that are not present in set B.

So, A - B = {5}

Now, A - (A - B)  will be the set that will contain all the elements of A that are not present in set A - B.

A - (A - B) = {6, 7}

A \cap∩ B will contain the elements that are present in both the sets A and B.

A \cap∩ B = {6, 7}

By looking at the answers above, we observe that both the sets are equal to each other i.e.

A - (A - B) =  A \cap∩ B = {6,7}