use a truth table to prove the rule of logic known as simplification.
$\frac{p wedge q}{p}$

construct and complete the truth table.

| p | q | premise $p wedge q$ | conclusion $p$ |
|---|---|-------------------------|-------------------|
| t | t | t | t |
| t | f | f | t |
| f | t | f | f |
| f | f | f | f |

how did you complete the truth table?

$\bigcirc$ a. the premise $p wedge q$ is only true when both $p$ and $q$ are true. the conclusion $p$ is the same as the second column.
$\bigcirc$ b. the premise $p wedge q$ is only true when both $p$ and $q$ are false. the conclusion $p$ is the same as the second column.
$\bigcirc$ c. the premise $p wedge q$ is only true when both $p$ and $q$ are true. the conclusion $p$ is the same as the first column.
$\bigcirc$ d. the premise $p wedge q$ is only false when both $p$ and $q$ are false. the conclusion $p$ is a the same as the first column.

Question

use a truth table to prove the rule of logic known as simplification.
$\frac{p wedge q}{p}$

construct and complete the truth table.

| p | q | premise $p wedge q$ | conclusion $p$ |
|---|---|-------------------------|-------------------|
| t | t | t                       | t                 |
| t | f | f                       | t                 |
| f | t | f                       | f                 |
| f | f | f                       | f                 |

how did you complete the truth table?

$\bigcirc$ a. the premise $p wedge q$ is only true when both $p$ and $q$ are true. the conclusion $p$ is the same as the second column.
$\bigcirc$ b. the premise $p wedge q$ is only true when both $p$ and $q$ are false. the conclusion $p$ is the same as the second column.
$\bigcirc$ c. the premise $p wedge q$ is only true when both $p$ and $q$ are true. the conclusion $p$ is the same as the first column.
$\bigcirc$ d. the premise $p wedge q$ is only false when both $p$ and $q$ are false. the conclusion $p$ is a the same as the first column.

Accepted Answer

# Brief Explanations:
1.  For the premise $p \land q$ (logical AND), it is only true if both $p$ and $q$ are true; otherwise, it is false.
2.  The conclusion column is just the value of $p$, which matches the first column of the table.
3.  Match this logic to the given options.

# Answer:
C. The premise p ∧ q is only true when both p and q are true. The conclusion p is the same as the first column.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer:

p	q	premise \\(p wedge q\\)	conclusion \\(p\\)
t	f	f	t
f	t	f	f
f	f	f	f