New Statements from Old

Negated statement of a statement is " Cows produce milk ". Write the original statement.

Negated statement of a statement is " $2\ge$$4$ ". Write the original statement.

Negated statement of a statement is " Ram scored higher marks than Bheem ". Write the original statement.

Negated statement of a statement is " Sky is not blue ". Write the original statement.

Negated statement of a statement is " Boy is not older than girl ". Write the original statement.

Solve the following problems related to three statements $\mathrm{p},\mathrm{q}$ and $\mathrm{r}$ :

If the truth value $\mathrm{r}$ is F and the truth value of the statement $~\left(~\mathrm{p}\vee ~\mathrm{q}\right)\wedge \left(~\mathrm{r}\right)$) is F, determine the truth value of the statement $\left(\mathrm{p}\wedge \mathrm{q}\right)$.

Solve the following problems related to three statements $\mathrm{p},\mathrm{q}$ and $\mathrm{r}$ :

The truth value of $~(\mathrm{p}\vee ~\mathrm{q})\wedge \mathrm{r}$ is T . Find the truth values of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$.

For two statements p and q if the truth value of $~(~\mathrm{p} \wedge ~\mathrm{q})$ is F, then what is truth value of $\mathrm{p}\wedge \mathrm{q}$ ?

Check whether the following pair of statements is negation of each other. Give reasons for your answer.

(i) $x+y=y+x$ is true for every real numbers $x$ and $y$.

(ii) There exist real numbers $x$ and $y$ for which $x+y=y+x$.

Write the negation of the following statement :

$s:$ All students study mathematics at the elementary level.

Write the negation of the following statement :

$r:$ All birds have wings.

Write the negation of the following statement:

$q:$ There exists a rational number $x$ such that $x^2=2$.

Write the negation of the following statement:

$p:$ For every real number $x,x^2>x$.

For the following compound statement, identify the connecting word and then break the given statement into its component statements :

For the following compound statement, identify the connecting word and then break the given statement into its component statements :

The sand heats up quickly in the sun and does not cool fast at night.

For the following compound statement, identify the connecting word and then break the given statement into its component statements:

Square of an integer is positive or negative.

For the following compound statement, identify the connecting word and then break the given statement into its component statements:

All rational numbers are real and all real numbers are not complex.

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

Write the following statements in symbolic form: Bob is rich but he is not happy.

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

Write the following statements in symbolic form: Bob is rich and happy.

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

Give verbal sentence to describe the following:

$R\wedge H$