Which of the following is a subset of {1, 3, 5, 7, 9}?
1.{3,5}    2.{7}    3.{ }    4. {1, 3, 5, 7, 9}     5. {2, 3}      6.{9}​.

Solution:

Given two sets, if all the members of the second set are also the members of the first set then the second set is a subset of the first set. The symbol of a subset is '⊆'. 

If all the members of Set B are the members of Set A, then Set B is known as a subset of Set A and is represented as B ⊆ A. Here, Set A is known as the superset of Set B.

Let U = {1, 3, 5, 7, 9}

⇒ 1.{3,5} ⊆ {1, 3, 5, 7, 9} ∵  3, 5 are members of U.   

⇒ 2.{7}  ⊆ {1, 3, 5, 7, 9} ∵  7 is a member of U.

⇒ 3.{ } ⊆ {1, 3, 5, 7, 9} ∵ all empty sets are subset of every set.

⇒ 4. {1, 3, 5, 7, 9} ⊂ {1, 3, 5, 7, 9} ∵ all members are members of U therefore it is a proper subset.

⇒ 5. {2, 3} ⊈ {1, 3, 5, 7, 9} ∵ 2 is not a member of U.

⇒ 6.{9}​ ⊆ {1, 3, 5, 7, 9} ∵ 9 is a member of U.

Thus, options 1, 2, 3, 6 are subsets of U, and 4 is a proper subset.

Which of the following is a subset of {1, 3, 5, 7, 9}?

Summary:

Options 1, 2, 3, and 6 are subsets of {1, 3, 5, 7, 9} and 4 is a proper subset.