Assertion - - p - q - p - q - - p - q Reason- p - q - p - q - q - p

The correct option is D Both assertion and reason are incorrect ∼( p↔ q ) ≡( p∧ q ) ∨( ∼ p∧ q ) #160; #160; p q #160; p↔ q #160; ...

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Byju's Answer

Standard IX

Mathematics

The Mid-Point Theorem

Assertion : ...

Question

Assertion : $\sim (p \leftrightarrow q) \equiv (p \land q) \lor (\sim p \land q)$ Reason: $p \leftrightarrow q \equiv (p \leftrightarrow q) \lor (q \leftarrow p)$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both assertion and reason are incorrect

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Solution

The correct option is D Both assertion and reason are incorrect
$\sim (p \leftrightarrow q) \equiv (p \land q) \lor (\sim p \land q)$

$p$ $q$ $p \leftrightarrow q$ $\sim (p \leftrightarrow q)$ $(p \land q)$ $\sim p$ $(\sim p \land q)$ $(p \land q) \lor (\sim p \land q)$
T T T F T F F T
T F F T F F F F
F T F T F T T T
F F T F F T F F
Therefore, assertion is incorrect.
$p \leftrightarrow q \equiv (p \leftrightarrow q) \lor (q \leftarrow p)$

$p$ $q$ $p \leftrightarrow q$ $p \leftrightarrow q$ $q \leftarrow p$ $(p \leftrightarrow q) \lor (q \leftarrow p)$
T T T T T T
T F F F T T
F T F F F F
F F T T T T
Therefore, Reason is also incorrect

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Similar questions

Assertion (A) Phenols give o-and p-nitrophenol on nitration with conc. $H N O_{3} a n d H_{2} S O_{4}$ mixture.
Reason (R) - OH group in phenol is o-,p-directing.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

Q. Assertion : Two events A and B are such that

P (A) = \frac{1}{3}

and

P (B) = \frac{2}{3}

then

P (A \cup B) \geq \frac{2}{3}

Reason : If

P (B) > P (A)

, then

P (A \cup B) \geq P (B)

Assertion (A) o-nitrophenol is less soluble in water than the m- and p-isomers.
Reason (R) m and p-nitrophenols exist as associated molecules.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

Q. Assertion: Three rational numbers between

\frac{2}{5} and \frac{3}{5} are \frac{9}{20}, \frac{10}{20} and \frac{11}{20}

.
Reason: A rational number between two rational numbers p and q is

\frac{1}{2} (p + q)

.
(a) Both Assertion and Reason are true and Reasom is a correct explanation of Assertion.
(b) Both Assertion and Reason and Reasom are true but Reasom is not a correct explanation of Assertion.
(c) Assertion is true and Reasom is false.
(d) Assertion is false and Reasom is true.

Assertion: $A B C D$ and $P Q R C$ are rectangles and $Q$ is the mid - point of $A C .$ Then $D P = P C .$

Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it.

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$p$	$q$	$p \leftrightarrow q$	$\sim (p \leftrightarrow q)$	$(p \land q)$	$\sim p$	$(\sim p \land q)$	$(p \land q) \lor (\sim p \land q)$
T	T	T	F	T	F	F	T
T	F	F	T	F	F	F	F
F	T	F	T	F	T	T	T
F	F	T	F	F	T	F	F

$p$	$q$	$p \leftrightarrow q$	$p \leftrightarrow q$	$q \leftarrow p$	$(p \leftrightarrow q) \lor (q \leftarrow p)$
T	T	T	T	T	T
T	F	F	F	T	T
F	T	F	F	F	F
F	F	T	T	T	T

Assertion :∼(p↔q)≡(p∧q)∨(∼p∧q) Reason: p↔q≡(p↔q)∨(q←p)

Assertion : $\sim (p \leftrightarrow q) \equiv (p \land q) \lor (\sim p \land q)$ Reason: $p \leftrightarrow q \equiv (p \leftrightarrow q) \lor (q \leftarrow p)$