Fallacy

Q. Consider
Statement I: $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.
Statement II: $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

1. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I

2. Statement I is true; Statement II is false

3. Statement I is false; Statement II is true
4. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

Q.

Find the component statements of the following compound statements.
'It is raining and it is cold'.

Q. The proposition $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is

1. Tautology and contradiction
2. Neither tautology nor contradiction
3. Tautology
4. Contradiction

Q. The statement $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is a:

1. Tautology and fallacy
2. Tautology
3. Fallacy
4. Neither tautology nor fallacy

Q.

Which one of the following relations on Z is equivalence relation?

1. 

2. 

3. 

4. 

Q. $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is

1. A tautology
2. A contradiction
3. Both a tautology and a contradiction
4. Neither a tautology nor a contradiction

Q. $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is ___.

1. Neither a tautology nor a fallacy
2. A tautology
3. A fallacy
4. Both a tautology and a fallacy

Q. $(p\wedge \sim q)\wedge (\sim p\vee q)$ is

1. A contradiction
2. A tautology
3. Either (a) or (b)
4. Neither (a) nor (b)

Q.

The statement $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is a:

1. Tautology

2. Fallacy

3. Neither tautology nor fallacy

4. Tautology and fallacy

Q. Which of the following is a fallacy?

1. $(p\wedge q)\wedge \sim (p\vee q)$
2. $p\vee (\sim p\wedge q)$
3. $(p\Rightarrow q)\Rightarrow p$
4. None of these

Q. The contrapositive of the statement ‘ If it is a Friday or if the sky is clear, then Sam plays’ is ___.

1. If Sam plays, then it is a friday or the sky is clear
2. If Sam does not play, then it is a Friday or the sky is clear
3. If Sam does not play, then it is not a Friday and the sky is not clear
4. If Sam does not play, then it is a Friday or the sky is not clear

Q. Re write each of the following statements in the form "p if and only if q"
(i) p : If you watch television then your mind is free and if your mind is free then you watch television
(ii) q : For you to get an A grade it is necessary and sufficient that you do all the homework regularly
(iii) r : If a quadrilateral is equiangular then it is a rectangle and if a quadrilateral is a rectangle then it is equiangular

Q. Find the modulus of the following complex numbers: (2+i)/(4i + (1+i) whole square.

Q. The proposition $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is

1. Tautology and contradiction
2. Neither tautology nor contradiction
3. Contradiction
4. Tautology

Q.

Which of the following is a fallacy?

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

2. None of these

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

4. $(p\Rightarrow q)\Rightarrow p$

Q. Consider
Statement I: $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.
Statement II: $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

1. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
2. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

3. Statement I is true; Statement II is false

4. Statement I is false; Statement II is true