Statement - 1- The statement p - q - p and - p - q are logically equivalent- Statement - 2- The end columns of the truth table of both statements are identical-A- Statement - 1 is false- Statement - 2 is trueB- Statement - 1 is true- Statement - 2 is true- Statement - 2 is not a correct explanation for Statement - 1C- Statement - 1 is true- Statement -2 is falseD- Statement - 1 is true- Statement - 2 is true- Statement - 2 is a correct explanation for Statement - 1

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Logical Connectives

Statement - 1...

Question

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.

Statement - 1 is false, Statement - 2 is true

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Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1

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Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1

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Statement - 1 is true, Statement - 2 is false

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Solution

The correct option is B Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1
Truth table has been given below:
$\begin{matrix} p & q & \sim p & p \lor q & (p \lor q) \land \sim p & \sim p \land q T & T & F & T & F & F T & F & F & T & F & F F & T & T & T & T & T F & F & T & F & F & F \end{matrix}$

Suggest Corrections

Similar questions

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.

Q. Statement - 1:

\sim (p \leftrightarrow\sim q)

is equivalent to

p \leftrightarrow q

.
Statement - 2:

\sim (p \leftrightarrow\sim 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 tautology.
Then which of the following statements is correct

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.

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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Statement - 1 : The statement (p∨q)∧∼p and ∼p∧q are logically equivalent. Statement - 2 : The end columns of the truth table of both statements are identical.

The correct option is B Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1Truth table has been given below: pq∼pp∨q(p∨q)∧∼p∼p∧qTTFTFFTFFTFFFTTTTTFFTFFF

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.