Problem 34
Answer: [tex]\boldsymbol{n(B) = 3}[/tex]
Reason:
We count the number of items inside set B. In this case there are 3 values, so that is why n(B) = 3
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Problem 36
Answer: [tex]\boldsymbol{n(A \cap C) = 1}[/tex]
Reason:
To be able to count the number of items inside set [tex]A \cap C[/tex], we first need to determine what this set looks like. In other words, we need to know the number(s) inside this set.
The upside down U symbol is the intersection symbol. It indicates we want to find what the sets A and C have in common. In this case, it's the value "4" and nothing else. This number is in both set A and set C at the same time. It might help to draw a venn diagram as you see below. I'm ignoring set B entirely since your teacher is not asking about the set in this problem.
We can then say [tex]A \cap C = \{4\}[/tex]
There's only one item inside this set, which is why [tex]n(A \cap C) = 1[/tex]
