Logical Connectives and Quantifiers

Check whether the ‘OR’ used in the following compound statement is exclusive or inclusive. Write the component statements and use them to check whether the compound statement is true or not. Justify your answer.

You are wet when it rains or you are in a river.

Let $R$ be the statement “Bob is rich” and $H$ be “Bob is happy”.

Give verbal sentence to describe the following:

$~H$

Let $R$ be the statement “Bob is rich” and $H$ be “Bob is happy”.

Give verbal sentence to describe the following:

$~R$

Identify the quantifier in the following statement: There exists a capital for every country in Europe.

Identify the quantifier in the following statement: There exists a mathematician who is not a man.

Identify the quantifier in the following statement: For every integer $n,\sqrt{n}$ is a real number.

What is the symbolic representation for all $x$ there exists a $y$?

Which of the following represents the qualifier "for all' ?

Consider two statements $P$ and $Q$ then which of the following represents the relation $P$ or $Q$ ?

What is the symbol of the logical connective 'Or'?

The negation of the statement, "All the students completed their homework" is "There exists a student who did not complete his homework".

The negation of the statement, "There exists a number which is equal to its square" is "There exists a number which is not equal to its square ".

The truth value of compound statement "The sand heats up quickly in the sun and does not cool down fast at night" is true.

What is 'if and only if' statement of “If you watch television then your mind is free and if your mind is free then you watch television.”

The negation of the statement "$(2+\sqrt{3})$ is a complex number" is

If$p,q,r$are statements with truth values $T,F,T$ respectively, then the truth value of the statement $\left(p\vee q\right)\to \left(q\vee r\right)$ is

If$p, q, r$ are statements with truth values $T, F, T,$ respectively, determine the truth values of the following:

$\left(r\wedge q\right)\leftrightarrow ~p$

If$p, q, r$ are statements with truth values $T, F, T,$ respectively, determine the truth values of the following:

$\left(p\to q\right)\vee r$

If$p, q, r$ are statements with truth values$T, F, T,$respectively, determine the truth value of the following:

$q\to \left(p\vee ~r\right)$

If $p,q,r$ are statements with truth values $T,F,T$ respectively. Then the truth value of $\left(~r\wedge p\right)\vee ~q$ is