Let U denote the set of all senators in Congress and let D={x ∈ U | x is a Democrat }

step 1 Okay, this question is focusing on subsets. It says for each of these pairs of sets, determine w

Let U denote the set of all senators in Congress and let ...

Let $U$ denote the set of all senators in Congress and let $$ \begin{array}{l} D=\{x \in U \mid x \text { is a Democrat }\} \\ R=\{x \in U \mid x \text { is a Republican\} } \\ F=\{x \in U \mid x \text { is a female }\} \\ L=\{x \in U \mid x \text { is a lawyer }\} \end{array} $$ Write the set that represents each statement. a. The set of all Democrats who are female or are lawyers b. The set of all senators who are not Democrats or are lawyers

Let $U$ denote the set of all senators in Congress and let
$$
\begin{array}{l}
D=\{x \in U \mid x \text { is a Democrat }\} \\
R=\{x \in U \mid x \text { is a Republican\} } \\
F=\{x \in U \mid x \text { is a female }\} \\
L=\{x \in U \mid x \text { is a lawyer }\}
\end{array}
$$
Write the set that represents each statement.
a. The set of all Democrats who are female or are lawyers
b. The set of all senators who are not Democrats or are
lawyers

Key Concepts

Set Builder Notation

A formal way to describe a set by specifying a property or rule that its elements must satisfy. This notation efficiently captures conditions like being a member of certain subsets defined by predicates or properties.

Set Complement

Set complement represents elements that do not belong to a specific set. It is useful for expressing conditions that exclude a particular group or satisfy a 'not' type condition.

Set Intersection

This operation represents the set of elements that belong to both sets simultaneously, akin to the logical 'and'. In problems where multiple criteria must be met (e.g., being a member of one category and another), intersection is used to combine these conditions.

Set Union

This operation combines elements from two sets, including those that are in either set, corresponding to the logical 'or'. It is used when a condition allows for membership in any one of several sets.

Transcript

00:01 Okay, this question is focusing on subsets.

00:06 It says for each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other.

00:18 And then we have three pairs of sets.

00:23 So let's start with the first one down here.

00:27 Our first set is going to be airline flights from new york to new delhi.

00:34 And our second set is nonstop flights from new york to new delhi.

00:37 So now, to be honest, this one is a little tricky for me because they kind of look the same, airline flights from new york to new delhi.

00:52 If it's going from new york to new delhi and nowhere else, it's probably nonstop.

01:00 But that being said, i'm going to define this as, our set a is airline flights from new york to new delhi.

01:12 That means someone, i'm going to define this as someone gets on in new york to fly and their final destination is new delhi.

01:22 So that's how i'm going to define it.

01:26 They get on in new york and their final destination is new delhi, but there may be some stops in the middle.

01:35 I don't know where those would be, but somewhere in between new york and new delhi, they get off a plane, they get on the next plane.

01:43 So these are the kinds of flights that i would take.

01:46 Ones with multiple stops because i'm poor.

01:49 The second one i'm going to define as, you get on new york and when you get off the first airplane, you're in new delhi.

01:59 So i would say, both achieve the same thing.

02:04 You can get on the plane in new york and get off in new delhi.

02:07 But i'm going to say that these nonstop flights are a subset of just all flights from new york to new delhi.

02:18 So b, in this case, b is a subset of a...

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