Question:
Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is
Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is
Show 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!
• $>$ turns directly into $\le$
• $<$ turns directly into $\ge$
Don't forget to flip the word "and" into "or" at the same time!
Updated On: Jun 12, 2026
- $3 + 6 \le 8$ or $2 + 3 < 6$
- $3 + 6 < 8$ or $2 + 3 < 6$
- $3 + 6 \le 8$ or $2 + 3 \ge 6$
- $3 + 6 > 8$ or $2 + 3 \ge 6$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The problem requires us to find the structural negation of a compound mathematical statement joined by the logical connective "and".
Step 2: Key Formula or Approach:
Let the component simple statements be: $p: 3 + 6 > 8$ $q: 2 + 3 < 6$ The given compound statement can be written symbolically as $p \land q$. According to De Morgan's Laws of logic, the negation of a conjunction is equivalent to the disjunction of the individual negations: $$\sim(p \land q) \equiv \sim p \lor \sim q$$
Step 3: Detailed Explanation:
1. Find the negation of the first statement $p$: $$\sim p: \text{Negation of } (3 + 6 > 8) \text{ is } (3 + 6 \le 8)$$ 2. Find the negation of the second statement $q$: $$\sim q: \text{Negation of } (2 + 3 < 6) \text{ is } (2 + 3 \ge 6)$$ 3. Apply De Morgan's Law by combining the negated components with an "or" ($\lor$) logical operator: $$\sim(p \land q) \equiv (3 + 6 \le 8) \text{ or } (2 + 3 \ge 6)$$
Step 4: Final Answer:
The negation of the statement corresponds to option (C).
The problem requires us to find the structural negation of a compound mathematical statement joined by the logical connective "and".
Step 2: Key Formula or Approach:
Let the component simple statements be: $p: 3 + 6 > 8$ $q: 2 + 3 < 6$ The given compound statement can be written symbolically as $p \land q$. According to De Morgan's Laws of logic, the negation of a conjunction is equivalent to the disjunction of the individual negations: $$\sim(p \land q) \equiv \sim p \lor \sim q$$
Step 3: Detailed Explanation:
1. Find the negation of the first statement $p$: $$\sim p: \text{Negation of } (3 + 6 > 8) \text{ is } (3 + 6 \le 8)$$ 2. Find the negation of the second statement $q$: $$\sim q: \text{Negation of } (2 + 3 < 6) \text{ is } (2 + 3 \ge 6)$$ 3. Apply De Morgan's Law by combining the negated components with an "or" ($\lor$) logical operator: $$\sim(p \land q) \equiv (3 + 6 \le 8) \text{ or } (2 + 3 \ge 6)$$
Step 4: Final Answer:
The negation of the statement corresponds to option (C).
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Mathematical Logic Questions
- If \((\sim p \wedge q)\rightarrow r\) is false, then the truth values of \(p,q,r\) respectively are
- If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:
- The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is
- Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink
- The logical expression \( [p \wedge (q \vee r)] \vee [\neg r \wedge \neg q \wedge p] \) is equivalent to
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions