To determine which statement is represented by [tex]\( p \wedge q \)[/tex], let's break down the given logical propositions and the meaning of the logical conjunction [tex]\( \wedge \)[/tex].
Given:
- [tex]\( p: -3 > -5 \)[/tex]
- [tex]\( q: 3 + 2 = 5 \)[/tex]
The symbol [tex]\( \wedge \)[/tex] represents the logical "and."
When we use [tex]\( p \wedge q \)[/tex], it means both [tex]\( p \)[/tex] and [tex]\( q \)[/tex] must be true for the entire statement to be true. Essentially, [tex]\( p \wedge q \)[/tex] states that both conditions must hold simultaneously.
Now, examining the options:
1. [tex]\(-3 > -5\)[/tex] or [tex]\(3 + 2 = 5\)[/tex]:
- This option uses "or" (disjunction), denoted by [tex]\( p \vee q \)[/tex], which means either [tex]\( p \)[/tex] is true or [tex]\( q \)[/tex] is true or both are true. This is not the correct conjunction [tex]\( \wedge \)[/tex].
2. [tex]\(-3 > -5\)[/tex] and [tex]\(3 + 2 = 5\)[/tex]:
- This option uses "and" (conjunction), denoted by [tex]\( \wedge \)[/tex], which means both [tex]\( p \)[/tex] and [tex]\( q \)[/tex] must be true at the same time, matching the definition of [tex]\( p \wedge q \)[/tex].
3. If [tex]\(-3 > -5\)[/tex] then [tex]\(3 + 2 = 5\)[/tex]:
- This option describes an implication, denoted by [tex]\( p \rightarrow q \)[/tex], which means if [tex]\( p \)[/tex] is true, then [tex]\( q \)[/tex] must also be true. This does not match the conjunction [tex]\( \wedge \)[/tex].
4. [tex]\(-3 > -5\)[/tex] if and only if [tex]\(3 + 2 = 5\)[/tex]:
- This option describes a biconditional, denoted by [tex]\( p \leftrightarrow q \)[/tex], which means [tex]\( p \)[/tex] is true exactly when [tex]\( q \)[/tex] is true, and vice versa. This also does not match the conjunction [tex]\( \wedge \)[/tex].
Therefore, the statement represented by [tex]\( p \wedge q \)[/tex] is:
[tex]\[
\boxed{-3 > -5 \text{ and } 3 + 2 = 5}
\][/tex]
