Logic Connectives, Compound Statement, Truth Table

The number of ordered triplets of the truth values of $p,q$ and $r$ such that the truth value of the statement $\left(p\vee q\right)\wedge \left(p\vee r\right)\Rightarrow \left(q\vee r\right)$ is True, is equal to

Statement $(P\Rightarrow Q)\wedge (R\Rightarrow Q)$ is logically equivalent to

The statement $\left(p\wedge \left(~q\right)\right)\vee \left(~p\right)$ is equivalent to 

$\left(P\Rightarrow Q\right)\vee \left(R\Rightarrow Q\right)$ is equivalent to

For the following compound statement, first identify the corresponding component statements. Then check whether the statements are true or not.

 If $a$ and $b$ are integers, then $ab$ is a rational number.

Identify the type of “Or” used in the following statements and check whether the statements are true or false:

To enter into a public library children need an identity card from the school or a letter from the school authorities.

Identify the type of 'or' (inclusive or exclusive) used in the statement "The school is closed if it is a holiday or a Sunday". Give reasons for your answer.

Find the component statements of the following and check whether they are true or not.

Find the component statements of the following and check whether they are true or not.

$2$ is a rational number or an irrational number.

Find the component statements of the following and check whether they are true or not.

Chandigarh is the capital of Haryana and UP.

Find the component statements of the following and check whether they are true or not.

A person who has taken Mathematics or Computer Science can go for MCA.

Find the component statements of the following compound statements:

Find the component statements of the following compound statements:

All rational numbers are real and all real numbers are complex.

Find the component statements of the following compound statements:

It is raining and it is cold.

Write the negation of the following statement and check whether the resulting statement is true,

The sum of $3$ and $4$ is $9$.

Write the negation of the following statement and check whether the resulting statement is true,

Write the negation of the following statement and check whether the resulting statement is true,

There does not exist a quadrilateral which has all its sides equal.

Write the negation of the following statement.

$\sqrt{7}$ is rational.

Let $p$ and $q$ be two propositions given by $p:$The sky is blue and $q:$milk is white. Then, $p\wedge q$ is given by

Construct the truth table of $p\wedge \left(p\wedge q\right)\to q$.