Determine whether the following propositions are true or false: (a) 5 is an odd number and 3 is a negative number. (b) 5 is an

Question

Determine whether the following propositions are true or false:
(a) 5 is an odd number and 3 is a negative number.
(b) 5 is an odd number or 3 is a negative number.
(c) 8 is an odd number or 4 is not an odd number.
(d) 6 is an even number and 7 is odd or negative.
(e) It is not true that either 7 is an odd number or 8 is an even number (or both).

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Jezebel 5 years 2021-08-10T04:18:15+00:00 1 Answers 437 views 0

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  1. Euphemia
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    2021-08-10T04:19:43+00:00
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    Answer:

    a) false

    b) true

    c) true

    d) true

    e) false

    Step-by-step explanation:

    In a statement of the type:

    p ∧ q

    where ∧ means “and”

    The statement is true only if both p and q are true

    the statement is false if p, q, or both, are false.

    and in the case of:

    p ∨ q

    where ∨ means “or”

    The statement is true if at least one of p or q (or both) are true.

    The statement is false if both are false.

    Now that we know that, let’s solve the problem:

    a) “5 is an odd number and 3 is a negative number.”

    Here we have:

    p = 5 is an odd number

    We know that this is true

    q = 3 is a negative number

    This is false.

    then the complete statement is false.

    b) “5 is an odd number or 3 is a negative number.”

    here we have:

    p = 5 is an odd number.

    this is true

    q = 3 is a negative number

    because in this case we have an “or”, with only p being true, the whole statement is true.

    c) “8 is an odd number or 4 is not an odd number.”

    p = 8 is an odd number  (this is false)

    q = 4 is not an odd number  (this is true, 4 is a even number)

    Again, we have an “or”, so we need only one true proposition, then the statement is true.

    d) “6 is an even number and 7 is odd or negative.”

    p = 6 is an even number  (true)

    q = 7 is odd or negative  (notice that we have an or, and 7 is odd is true, so this proposition is true)

    Then both propositions are true, then the statement is true.

    e) “It is not true that either 7 is an odd number or 8 is an even number (or both).”

    This is most complex, this will be true if at least one of the propositions is false.

    but:

    7 is an odd number is true

    8 is an even number is true.

    Then both statements are true, which means that the statement is false.

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