Answer:
1. True
2. True
3. True
4. False
5. False
6. False
7. True
8. False
9. True
10. False
Explanation:
∈ means "is an element of"
⊂ means "only contains some, but not all, the elements of"
⊆ means "only contains some, possibly all, the elements of"
If one of those symbols is strickenthrough, it simply means the opposite, e.g. "it's not true that it's an element of" or "it's not true that it only contains some, (...) the elements of"
∅ is an empty set
{ something } is a set containing everything inside the curly brackets. Thus, { } is an empty set.
Let's rewrite the statements:
1. 5 is an element of {1, 3, 5, 7, 9}
TRUE
2. 4 is not an element of {1, 3, 9}
TRUE
3. {5, 6, 7} only contains some, possibly all, the elements of {5, 6, 7}
TRUE
4. {1, 2, 3} only contains some, but not all, the elements of {1, 2, 3}
FALSE (it contains all)
5. it's not true that {9} only contains some, possibly all, the elements of {9, 10}
FALSE (it does only contain elements of {9, 10} )
6. it's not true that 8 is an element of {2,4,6,8,10}
FALSE (because it is an element of that set)
7. empty set only contains some, possibly all, the elements of empty set
TRUE (it contains only elements of empty set - all of them, namely none)
8. 0 is an element of empty set
FALSE (empty set is empty, so it cannot contain 0)
9. {13, 11} only contains some, but not all, the elements of {11, 12, 13}
TRUE (order is irrelevant)
10. {7, 8} only contains some, possibly all, the elements of {8}
FALSE (7 is not an element of {8} )