Question

identify if each statement is true or false. Write your answer in the space provided.
Given: U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1. The universal set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
2. {2, 4, 6, 8, 10 is a subset of U.
3. {0, 10) is a subset of U.
4. Empty set { } is a subset of U.
5. The cardinality number of set U is 10.​

Answer 1

Step-by-step explanation:  

Given: U= {$1, 2, 3, 4, 5, 6, 7, 8, 9, 10$}  

1. The universal set is {$1, 2, 3, 4, 5, 6, 7, 8, 9, 10$}.  

2. {$2, 4, 6, 8, 10$} is a subset of U.  

3. {$0, 10$} is a subset of U.  

4. Empty set { } is a subset of U.  

5. The cardinality number of set U is $10$.​  

To Find: If the statements are true or False  

• We know, Universal set is denoted by the Letter 'U', Hence, The universal set is {$1, 2, 3, 4, 5, 6, 7, 8, 9, 10$} as it is given in the question. Therefore, option 1 is True.

• We also know that a set is a subset of another set if all the elements of the subset are in the super set.

     ⇒ Since, All the elements of set {$2,4,6,8,10$} are contained in the universal set, {$2,4,6,8,10$} is a subset of U. Therefore, option 2 is also true.  

    ⇒ Since the element 0 of set {$0, 10$} is not in set U, the set {$0, 10$} is not a subset of U. Hence, option 3 is false.  

    ⇒  We know that empty set is a subset of every set. So, option 4 is true.  

The cardinality number also denoted by n(A) for a set A, is the number of elements in the set A. The cardinality number of set U is 10 as it has 10 elements. Hence, option 5 is also true.

Answer 2

Answer:

1:true

2:true

3:false

4:true

5:true