Subsets questions with answers

Questions

1. Question 1Subset or proper subset?

   $A = \{1, 3\}$ and $B = \{1, 3, 5, 7, 9\}$. State whether $A \nsubseteq B$ is true or false.

   Show the worked solution

   1. Step 1: Is every element of A also in B?Yes: every element of $A$ is in $B$, so $A \subseteq B$.
   2. Step 2: So the statement isThe statement is false.
2. Question 2Subset or proper subset?

   $A = \{5, 10, 15, 20\}$ and $B = \{5, 10, 15, 20\}$. State whether $A \subset B$ is true or false.

   Show the worked solution

   1. Step 1: Is every element of A also in B?Yes: every element of $A$ is in $B$, so $A \subseteq B$.
   2. Step 2: Does B have an element that A doesn't?No: $A = B$, so $A$ is not a proper subset of $B$.
   3. Step 3: So the statement isThe statement is false.
3. Question 3Tricky statements: ⊂, ⊆, ∈ and ∅

   $A = \{5, 10, 15\}$. State whether $\{5\} \subseteq A$ is true or false.

   Show the worked solution

   1. Step 1: ∈ compares an element with a set; ⊆ and ⊂ compare two setsThe set containing the number is a subset: its one element is in $A$.
   2. Step 2: So the statement isThe statement is true.
4. Question 4Tricky statements: ⊂, ⊆, ∈ and ∅

   $A = \{2, 3, 5, 7\}$ and $B = \{7, 5, 3, 2\}$. State whether $B \subseteq A$ is true or false.

   Show the worked solution

   1. Step 1: ∈ compares an element with a set; ⊆ and ⊂ compare two sets$B$ has exactly the same elements as $A$ (order doesn't matter), so $B = A$ and $B \subseteq A$.
   2. Step 2: So the statement isThe statement is true.