Determine whether the following propositions are true or false, and briefly expl

Question

Determine whether the following propositions are true or false, and briefly explain your reasoning. 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 a an even number and 7 is odd or negative. e. It is not true that 7 is an odd number or 8 is an even number. Give a truth table for the following propositions. In this class you are required to create and fill in a column for every sub-expression (portion of a compound proposition) For part a, start by creating a four-row truth table, with propositional variables p and g. Fill out all the possible truth values for these two variables in the canonical order, as shown in the textbook (See the paragraph that starts "Note that the T and F values for each row are unique, and that they are chosen methodically ... "). Then create a column for not p. Then for part a, create a column for (not p logicalor q). Then to complete part a, create a column for p logicaland (not p logicalor q). For the other pans, create an eight-row truth table, with the propositional variables p, q, and s: Fill out all the possible truth values for these three variables in the canonical order as before. Create a column for p logicaland q. Then create a column for (p logicaland q) V S. Follow the same procedure for creating columns for each subexpression of each of the remaining parts of this exercise. We've provided truth table templates for you to work on, on the next page

Explanation / Answer

// As per chegg policy, I will be answering the first full question

5)a)

x = {5 is odd} = {true}

y = {3 is negative} = {false}

ans = x & y = {true} & {false} = false

5)b)

x = {5 is odd} = {true}

y = {3 is negative} = {false}

ans = x & y = {true} | {false} = true

5)c)

x = {8 is odd} = {false}

y = {4 is not odd} = {true}

ans = x | y = {false} & {true} = true

5)d)

x = {6 is even} = {true}

y = {7 is odd or negative} = {true | false} = {true}

ans = x & y = {true} & {true} = true

5)e)

x = {7 is odd} = {true}

y = {8 is even} = {true}

ans = !(x | y) = !({true} | {true}) = !{true)}= false

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