Tautology

Q.

If $P$ and $Q$are two statements, then which of the following compound statement is a tautology?

1. $\left(\right(P\Rightarrow Q)\wedge ~Q)\Rightarrow P$

2. $\left(\right(P\Rightarrow Q)\wedge ~Q)\Rightarrow ~P$

3. $\left(\right(P\Rightarrow Q)\wedge ~Q)$

4. $\left(\right(P\Rightarrow Q)\wedge ~Q)\Rightarrow Q$

Q.

What Is The Meaning Of The Idiom / Phrase: The Pros And Cons.

Q. The conditional $(p\wedge q)\Rightarrow p$ is ___.

1. A tautology
2. A fallacy
3. Neither a tautology nor a fallacy
4. A contrapositive

Q.

Which of the following is not a tautology ?

1. $(p\Rightarrow q)\Rightarrow (\sim q\Rightarrow \sim p)$

2. $p\vee \sim (q\wedge \sim q)$

3. $p\vee \sim p$

4. $p\wedge (q\vee \sim q)$

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

1. Statement - 1 is true, Statement - 2 is true;
   Statement - 2 is not a correct explanation for statement - 1.
2. Statement - 1 is true, Statement - 2 is false.
3. Statement - 1 is false, Statement - 2 is true.
4. Statement - 1 is true, Statement - 2 is true,
   Statement - 2 is a correct explanation for statement - 1.

Q. Which of the following is a tautology?

1. $(\sim q\wedge p)\wedge q$
2. $(\sim q\wedge p)\wedge (p\wedge \sim p)$
3. $(\sim q\wedge p)\vee (p\vee \sim p)$
4. $(p\wedge q)\wedge (\sim (p\wedge q\left)\right)$

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

1. Statement - 1 is true, Statement - 2 is true;
   Statement - 2 is not a correct explanation for statement - 1.
2. Statement - 1 is true, Statement - 2 is false.
3. Statement - 1 is false, Statement - 2 is true.
4. Statement - 1 is true, Statement - 2 is true,
   Statement - 2 is a correct explanation for statement - 1.

Q.

The statement $(p\to q)\to \left[\right(\sim p\to q)\to q]$ is

1. a tautology

2. equivalent to $\sim p\to q$

3. a fallacy

4. equivalent to $p\to \sim q$

Q.

Which of the following is not a tautology ?

1. $p\vee \sim p$

2. $(p\Rightarrow q)\Rightarrow (\sim q\Rightarrow \sim p)$

3. $p\vee \sim (q\wedge \sim q)$

4. $p\wedge (q\vee \sim q)$

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

1. Both Statement 1 and Statement 2 are true and Statement 2 is a correct explanation for statement 1
2. Both Statement 1and Statement 2 are true and Statement 2 is not a correct explanation for Statement 1
3. Statement 1 is false but Statement 2 is true
4. Statement 1 is true but statement 2 is false

Q. Which of the following is not a tautology ?

1. $p\vee \sim p$
2. $p\vee \sim (q\wedge \sim q)$
3. $p\wedge (q\vee \sim q)$
4. $(p\Rightarrow q)\Rightarrow (\sim q\Rightarrow \sim p)$

Q. Choose the correct option.
Statement $1:(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.
Statement $2:(p\Rightarrow q)\iff (\sim q\Rightarrow \sim p)$ is a tautology.

1. Both the statements are TRUE and STATEMENT $2$ is the correct explanation of STATEMENT $1.$
2. Both the statements are TRUE but STATEMENT $2$ is NOT the correct explanation of STATEMENT $1.$
3. STATEMENT $1$ is TRUE and STATEMENT $2$ is FALSE.
4. STATEMENT $1$ is FALSE and STATEMENT $2$ is TRUE.

Q. Statements $(p\to q)\leftrightarrow [\{(p\wedge \sim q)\wedge t\}\vee c]$ is

1. Tautology
2. Contradiction
3. Neither tautology nor contradiction
4. Can't say anything