Class 11th Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen Exemplar Solution Maths Mathematical Reasoning

Write the negation of the following simple statements:

i. The number 17 is prime.

ii. 2 + 7 = 6.

iii. Violets are blue.

iv. $\sqrt$ 5 is a rational number.

v. 2 is not a prime number.

vi. Every real number is an irrational number.

vii. Cow has four legs.

viii. A leap year has 366 days.

ix. All similar triangles are congruent.

x. Area of a circle is the same as the perimeter of the circle.

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Payal Gupta | Contributor-Level 10

7 months ago

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l} (i) T h e n u m b e r 17 i s n o t p r i m e . \\ (i i) 2 + 7 \neq 6 . \\ (i i i) V i o l e t s a r e n o t b l u e . \\ (i v) \sqrt[]{5} i s n o t a r a t i o n a l n u m b e r . \\ (v) 2 i s a p r i m e n u m b e r . \\ (v i) E v e r y r e a l n u m b e r i s n o t a n i r r a t i o n a l n u m b e r . \\ (v i i) C o w d o e s n o t h a v e f o u r l e g s . \\ (v i i i) A l e a p y e a r d o e s n o t h a v e 366 d a y s . \\ (i x) T h e r e e x i s t s i m i l a r t r i a n g l e s w h i c h a r e n o t c o n g r u e n t . \\ (x) A r e a o f a c i r c l e i s n o t s a m e a s t h e p e r i m e t e r o f t h e c i r c l e . \end{array}$

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Let $Δ, \nabla \in {\land, \lor}$ be such that $p \nabla q \Rightarrow ((p Δ q) \nabla r)$ is a tautology. Then $(p \nabla q) Δ r$ is logically equivalent to:

Case – I $Δ \equiv \nabla \equiv \land$

$(p \land q) \to ((p \land q) \land r)$

it can be false if r is false,

so not a tautology

&n

Negation of the Boolean statement $(p \lor q) \Rightarrow ((\sim r) \lor p)$ is equivalent to

pva $(\sim r v p)$

$\sim (p \lor q) \lor (\sim r v p)$

its negation as asked in question

$(p \lor q) \land (\sim p \land r)$

= $(p \land \sim p \land r) \lor (q \land r \land \sim p)$

= $(p \land r \land \sim p) [a s p \land \sim p i s f a l s e]$

The remainder when (2021)²⁰²³ is divided by 7 is:

$2021 \equiv - 2$ mod (7)

$\Rightarrow {(2021)}^{2023} \equiv {(- 2)}^{2023} m o d (7)$ …… (i)

Now, ${(- 2)}^{3} \equiv - 1 m o d (7)$

$\Rightarrow {(- 2)}^{2023} \equiv (- 2) m o d (7) \equiv 5 m o d (7)$ ……. (ii)

(i) & (ii)

$\Rightarrow {(2021)}^{2023} \equiv 5 m o d (7)$

$∴$ Remainder = 5

Let p, q, r be three logical statements. Consider the compound statements

$S_{1} : ((\sim p) \lor q) \lor ((\sim p) \lor r) a n d$

$S_{2} : p \to (q \lor r)$

Then, which of the following is NOT true?

kindly consider the following Image

The statement $(\sim (p \Leftrightarrow \sim q)) \land q i s :$

$\sim (p \Leftrightarrow \sim q) \land q = (p \Leftrightarrow \sim q) \land q i s :$

$∴ (\sim (P \Leftrightarrow \sim Q)) \land$ q is equivalent to $(p \Rightarrow q) \land$

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Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen 2025

Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen 2025

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