Question

Determine whether these two statements are logically equivalent by constructing truth tables. -(PA-Q) and PvQ After you construct truth tables, explain why they are logically equivalent or not. Note for table construction: . Select table icon to draw a table . Select fx icon (left of "Mashups") to enter symbols for AND, OR NOT. They are located in the second group from the left. • Choose appropriate sizes for rows and columns; both width and height can be set about 150; increase them if you need more space. . You may set cell-padding and cell-spacing both 1; border 1. T T T Arial 3(12pt) T. E. E. Path: P ek Save and submit to save and submit. Click Save All Answers to save all answers, Type here to search

Answer 1

The statement
`\\eg(p \land \\eg q)` and the statement
`\\eg p \lor q` are logically equivalent.

Explanation:

You use truth tables to determine how the truth or falsity of a complex statement depends on the truth or falsity of its components.

There are four steps to building a truth table:

1. Determine the number of different propositions in the statement, for this case two (p and q)
2. The main operators have to be identified.

For the first statement we have:

`\\eg (p \land\\eg q)` two operators and (
`\land`) and not (
`\\eg`).

For the second statement
`\\eg p \lor q` we have two operators or (
`\lor`) and not (
`\\eg`)

3. Next, the basic input values are assigned to each letter.

4. The final step is to calculate the values of each logical operator.

Following these steps, we can generate the truth table.

Two statements are logically equivalent if, and only if, their resulting forms are logically equivalent when identical statement variables are used to represent component statements.

We can see from the truth table that the statement
`\\eg(p \land \\eg q)` and
`\\eg p \lor q` have the same truth values, so they are logically equivalent.