Compound Statement

Q.

If p: Arjun is the fastest q: Azad is the captain. Then which of the following denotes the compound statement: "Arjun is the fastest OR Azad is not the captain”

1. 

2. 

3. 

4. 

Q.

A simple statement can be a combination of 2 or more simple statements

1. False

2. True

Q. If p : It rains today, q : I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition :
If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie

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

Q. The logically equivalent proposition of $p\iff q$ is

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

Q. The statement $\sim (p\leftrightarrow \sim q)$ is

1. equivalent to $p\leftrightarrow q$
2. a tautology
3. a fallacy
4. equivalent to $\sim p\leftrightarrow q$

Q. The Boolean expression $(p\wedge \sim q)\vee q\vee (\sim p\wedge q)$ is equivalent to

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

Q. "11 is the fifth prime number."This is a statement.

1. simple
2. compound
3. none

Q. The logical statement $\left[\right(p\wedge q)\to p]\to (q\wedge \sim q)$ is

1. a tautology
2. a contradiction
3. neither a tautology nor a contradiction
4. equivalent to $p\vee q$

Q. Which among the following statements have truth value as FALSE
$A)13$ is odd number and prime number
$B)23$ is even number and prime number
$C)$ Volume of sphere is $\frac{4}{3}\pi r^3$ cubic units and surface area is $\pi r^2$ sq. units

1. $B$ and $C$
2. $A$ and $B$
3. $A$ and $C$
4. $A,B$ and $C$

Q. For the statement "A mixture of alcohol and water can be separated by chemical methods" which among the following option is correct

1. It is compound statement having connective ${}^{\prime \prime }O{R}^{\prime \prime }$
2. It is compound statement having connective ${}^{\prime \prime }AN{D}^{\prime \prime }$
3. It is a simple statement
4. It is not a statement