To solve the problem of writing the negation of the statement [tex]\(2 < 3 \text{ or } 3 \neq 13\)[/tex] using De Morgan's Law, let’s proceed with the following steps:
1. Understand the given statement:
- The original statement is [tex]\(2 < 3 \text{ or } 3 \neq 13\)[/tex].
2. Recall De Morgan’s Law:
- De Morgan's Laws provide rules for negating expressions involving logical operators. Specifically, one of De Morgan’s Laws states that the negation of [tex]\((A \text{ or } B)\)[/tex] is [tex]\((\neg A \text{ and } \neg B)\)[/tex].
3. Apply De Morgan's Law:
- Negate the entire statement [tex]\(2 < 3 \text{ or } 3 \neq 13\)[/tex] to use De Morgan’s Law:
[tex]\[
\neg (2 < 3 \text{ or } 3 \neq 13)
\][/tex]
- According to De Morgan’s Law, this becomes:
[tex]\[
\neg (2 < 3) \text{ and } \neg (3 \neq 13)
\][/tex]
4. Negate each individual part:
- Negate [tex]\(2 < 3\)[/tex]:
[tex]\[
\neg (2 < 3) \implies 2 \geq 3
\][/tex]
- Negate [tex]\(3 \neq 13\)[/tex]:
[tex]\[
\neg (3 \neq 13) \implies 3 = 13
\][/tex]
5. Combine the results:
- From the above steps, we get:
[tex]\[
2 \geq 3 \text{ and } 3 = 13
\][/tex]
So, the negation of the statement [tex]\(2 < 3 \text{ or } 3 \neq 13\)[/tex] is [tex]\(2 \geq 3 \text{ and } 3 = 13\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{B \text{. } 2 \geq 3 \text{ and } 3 = 13} \][/tex]
