Question

Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is

• A. $3 + 6 \le 8$ or $2 + 3 < 6$
• B. $3 + 6 < 8$ or $2 + 3 < 6$
• C. $3 + 6 \le 8$ or $2 + 3 \ge 6$
• D. $3 + 6 > 8$ or $2 + 3 \ge 6$

Hint:

When negating mathematical inequalities, remember that the strict inequality symbol flips completely and gains or loses an equality bar:

• $>$ turns directly into $\le$

• $<$ turns directly into $\ge$
Don't forget to flip the word "and" into "or" at the same time!

Answer 1

The Correct Option is C

Step 1: Name the two simple statements.
Let $p: 3 + 6 > 8$ and $q: 2 + 3 < 6$. The given compound statement is $p \wedge q$ (p AND q).
Step 2: Recall De Morgan's law.
The negation of a conjunction turns AND into OR and negates each piece: $\sim(p \wedge q) = (\sim p) \vee (\sim q)$.
Step 3: Negate the first part.
The opposite of $3 + 6 > 8$ is $3 + 6 \le 8$.
Step 4: Negate the second part.
The opposite of $2 + 3 < 6$ is $2 + 3 \ge 6$.
Step 5: Join with OR.
By De Morgan, the negation is ($3 + 6 \le 8$) OR ($2 + 3 \ge 6$).
Step 6: Match to the option.
This is exactly $3 + 6 \le 8$ or $2 + 3 \ge 6$.
\[ \boxed{3 + 6 \le 8 \;\text{or}\; 2 + 3 \ge 6} \]