To write the given conditional statements in their symbolic forms, we need to identify how each statement translates into logical notation. Here we use:
- [tex]\( p \)[/tex] for "Today is October 6."
- [tex]\( q \)[/tex] for "Today is Nina's birthday."
We'll also use:
- [tex]\(\neg p\)[/tex] for "Today is not October 6."
- [tex]\(\neg q\)[/tex] for "Today is not Nina's birthday."
Let's match each statement to its symbolic form:
1. If it is not Nina's birthday, then today is not October 6.
- This translates to: [tex]\(\neg q \rightarrow \neg p\)[/tex]
2. If today is not October 6, then it is not Nina's birthday.
- This translates to: [tex]\(\neg p \rightarrow \neg q\)[/tex]
3. If today is Nina's birthday, then it is October 6.
- This translates to: [tex]\(q \rightarrow p\)[/tex]
4. If today is October 6, then it is Nina's birthday.
- This translates to: [tex]\(p \rightarrow q\)[/tex]
Let’s put them in order with the correct matching:
1. If it is not Nina's birthday, then today is not October 6.
- Symbolic form: [tex]\(\neg q \rightarrow \neg p\)[/tex]
2. If today is not October 6, then it is not Nina's birthday.
- Symbolic form: [tex]\(\neg p \rightarrow \neg q\)[/tex]
3. If today is Nina's birthday, then it is October 6.
- Symbolic form: [tex]\(q \rightarrow p\)[/tex]
4. If today is October 6, then it is Nina's birthday.
- Symbolic form: [tex]\(p \rightarrow q\)[/tex]
Thus, the matching should be written as follows:
1. [tex]\(\neg q \rightarrow \neg p\)[/tex] [tex]$\square$[/tex]
2. [tex]\(\neg p \rightarrow \neg q\)[/tex] [tex]$\square$[/tex]
3. [tex]\(q \rightarrow p\)[/tex] [tex]$\square$[/tex]
4. [tex]\(p \rightarrow q\)[/tex] [tex]$\square$[/tex]
