Respuesta :
Answer:
a) [tex]\bar{A}[/tex]
b) [tex]A\cap B[/tex]
c) [tex]A-B[/tex]
d) [tex]\overline{A\cup B}[/tex]
e) [tex]A\oplus B[/tex]
Step-by-step explanation:
We are given the following in the question:
A: English words that contain the letter x
B: English words that contain the letter q
a) The set that represents English words that do not contain the letter x is
[tex]\bar{A}[/tex]
That is complement of A.
The compliment of A contains all the observation that cannot belong to A.
[tex]x \in \bar{A} \Rightarrow x\notin A[/tex]
b) The set of English words that contain both an x and a q
This is represented by the intersection of both the sets.
The intersection consist of terms common to both sets.
c) The set of English words that contain an x but not a q
This is represented by
[tex]A-B\\x \in A-B \Rightarrow x \in A, x \notin B[/tex]
d) The set of English words that do not contain either an x or a q.
This will be represented by the compliment of union of the two sets.
[tex]\overline{A\cup B}\\x \in \overline{A\cup B} \Rightarrow x \notin A\cup B[/tex]
e) The set of English words that contain an x or a q, but not both.
This will be represented by the symmetric difference of the two sets.
[tex]A\oplus B\\x \in A\oplus B \Rightarrow x\in A, x\in B,x \notin A\cap B[/tex]
The set of English words that contain an x but not a q can be represented as [tex]x = \overline{A\cap B}, x \notin A\cup B[/tex].
What is a set?
A set is a mathematical model for a collection of diverse things; it comprises elements or members, which can be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
As it is given to us that A is the set of English words that contain the letter x and B is the set of English words that contain the letter q.
A.)
Let the set [tex]\bar A[/tex] be the complement of set A. Therefore, the complement of A which contains all the observations that cannot belong to A can be written as,
[tex]x\in \bar{A} \implies x\notin \bar{A}[/tex]
B.)
This can be represented by the intersection of both sets. therefore, the intersection will consist of terms that are common to both sets. It can be represented as,
[tex]A \cap B[/tex]
C.)
The set of English words that contain an x but not a q can be represented as,
[tex]A-B\\x\in A-B \implies x\in {A}, x\notin {B}[/tex]
D.)
The complement of the union of the two sets can be used to represent the set of English words that do not contain either an x or a q.
[tex]\overline{A\cap B}\\x = \overline{A\cap B}, x \notin A\cup B[/tex]
E.)
The symmetric difference between the two sets can be used to represent the set of English words that contain an x or a q, but not both.
[tex]A \oplus B\\x \in A \oplus B, x\in A, x\in B, x \notin A\cap B[/tex]
Hence, the set of English words that contain an x but not a q can be represented as [tex]x = \overline{A\cap B}, x \notin A\cup B[/tex].
Learn more about Sets:
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