Question

I need an explanation of the answers for the following examples if someone can please:

A={1, 3, 5, 7} B={1, 3, 5, 7, 9}

is A a subset of B?

Are all elements/components of A found in B?

Are all elements/components of B found in A?

is A a proper subset of B?

Answer 1

As A a subset of B?

Yes, by definition, A is a subset of B if every element of A is also an element of B.

Are all elements/components of A found in B?

Yes, this is exactly what makes A a subset of B.

Are all elements/components of B found in A?

No: all elements of B are also elements of A except for 9, who only belongs to B.

is A a proper subset of B?

Yes, because there are elements in B that are not elements of A.

Answer 2

Answer: The answer is as follows:

Explanation:

(a) yes, Set A is a subset of Set B.

Because all the elements of Set A are present in Set B. Therefore, A is a subset of Set B.

(b) Yes, all the elements of Set A found in Set B. In the above example, elements of Set A = {1,3,5,7} are present in Set B.

(c) No, all the elements of Set B are not found in Set A. Infact, all the elements of Set B are found in Set A except element {9}.

(d) Yes, Set A is a proper subset of B. According to the definition of proper subset, a Set A to be proper subset of B, then all the elements of Set A are present in Set B, but set B contains atleast one element that is not present in Set A. In our case, there is one element that is not present in Set A and that is {9}.