Let A be the set of English words that contain the letter x, and let B be the set of English words that contain the letter q. Express each o

Question

Let A be the set of English words that contain the letter x, and let B be the set of English words that contain the letter q. Express each of these sets as a combination of A and B.

a) The set of English words that do not contain the letter x.
b) The set of English words that contain both an x and a q.
c) The set of English words that contain an x but not a q.
d) The set of English words that do not contain either an x or a q.
e) The set of English words that contain an x or a q, but not both.

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Lyla 6 days 2021-10-08T10:59:34+00:00 1 Answer 0

Answers ( )

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    2021-10-08T11:01:16+00:00

    Answer:

    a) \bar{A}

    b) A\cap B

    c) A-B

    d) \overline{A\cup B}

    e) A\oplus B

    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

    \bar{A}

    That is complement of A.

    The compliment of A contains all the observation that cannot belong to A.

    x \in \bar{A} \Rightarrow x\notin A

    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

    A-B\\x \in A-B \Rightarrow x \in A, x \notin B

    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.

    \overline{A\cup B}\\x \in \overline{A\cup B} \Rightarrow x \notin A\cup B

    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.

    A\oplus B\\x \in A\oplus B \Rightarrow x\in A, x\in B,x \notin A\cap B

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