Statement 1- -p-q is equivalent to p-qStatement 2 -p-q is a tautology

The correct option is D Statement 1 is true but statement 2 is falsepq #160; #160; #160; #160; #160; ∼ p #160; #160; #160; #160; ...

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Byju's Answer

Standard XI

Mathematics

Tautology

Statement 1: ...

Question

Statement 1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$
Statement 2 $:\sim (p \leftrightarrow\sim q)$ is a tautology

Both Statement 1 and Statement 2 are true and Statement 2 is a correct explanation for statement 1

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Both Statement 1and Statement 2 are true and Statement 2 is not a correct explanation for Statement 1

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Statement 1 is true but statement 2 is false

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Statement 1 is false but Statement 2 is true

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Solution

The correct option is D Statement 1 is true but statement 2 is false
p q $\sim p$ $\sim q$ $p \leftrightarrow\sim q$ $\sim (p \leftrightarrow\sim q)$
$p \leftrightarrow q$
T T F F F T T
T F F T T F F
F T T F T F F
F F T T F T T

Clearly, $\sim (p \leftrightarrow\sim q)$ is not a tautology because it does not contain T in the column of its truth table. Also, $\sim (p \leftrightarrow\sim q)$ & $p \leftrightarrow q$ have the same truth value
Hence, option 'C' is correct.

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Similar questions

Statement 1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$
Statement 2: $\sim (p \leftrightarrow\sim q)$ is tautology.
Then which of the following statements is correct

Q. Statement - 1:

\sim (p \leftrightarrow\sim q)

is equivalent to

p \leftrightarrow q

.
Statement - 2:

\sim (p \leftrightarrow\sim q)

is a tautology.

Choose the correct option.

Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

Q. Statement - 1 : The statement

(p \lor q) \land \sim p

and

\sim p \land q

are logically equivalent.
Statement - 2 : The end columns of the truth table of both statements are identical.

Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number if and only if y is a transcendental number”.
Statement-1 : $r i s e q u i v a l e n t t o e i t h e r q o r p$
Statememt-2 : $r i s e q u i v a l e n t t o (p \leftrightarrow\sim q)$

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

Statement 1: ∼(p↔∼q) is equivalent to p↔qStatement 2 :∼(p↔∼q) is a tautology

Statement 1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$
Statement 2 $:\sim (p \leftrightarrow\sim q)$ is a tautology