Statements

Define an open statement. Find the truth value of open statement $3x=9$ at $x=3$.

Define an open statement. Find the truth value of open statement $3x=9$ at $x=2$.

Define an open statement. Find the truth value of open statement $x^2+2=11$ at $x=-3$.

Define an open statement. Find the truth value of open statement $x^2+2=5$ at $x=1$.

Define an open statement. Find the truth value of open statement $x+2=5$ at $x=1$.

By giving counter-examples, show that the following statements are false :

For two real numbers $\mathrm{a}$ and $\mathrm{b}$, if $\left|\mathrm{a}\right|\mathrm{b}\ge 0$, then $\left|\mathrm{b}\right|\mathrm{a}\ge 0$.

By giving counter-examples, show that the following statements are false :

If all the angles of a triangle are equal then the triangle is an obtuse-angled triangle.

By giving counter-examples, show that the following statements are false :

For any two imaginary numbers $\mathrm{x}$ and$\mathrm{y}, (\mathrm{x} + \mathrm{y})$ is an imaginary number.

By giving counter-examples, show that the following statements are false :

For any real numbers $\mathrm{a}, \mathrm{b}$ and $\mathrm{x}, {\mathrm{x}}^{\mathrm{a}} = {\mathrm{x}}^{\mathrm{b}}$ implies that $\mathrm{a} = \mathrm{b}$.

By giving counter-examples, show that the following statements are false :

For any real numbers $\mathrm{a}$ and $\mathrm{b}$$, {\mathrm{a}}^2={\mathrm{b}}^2$ implies that $\mathrm{a} = \mathrm{b}$.

By giving counter-examples, show that the following statements are false :

If $\mathrm{n}$ is an odd integer, then $\mathrm{n}$ is prime.

If for a statement $\mathrm{p}$ the truth value of $~\mathrm{p}$ is $\mathrm{F}$, then a possible choice of $\mathrm{p}$ is the statement.

${\sin }^{2}x+{\cos }^{2}x=0$ is a statement.

The sentence 'Every square is a rectangle' is a statement.

The sentence ''Every set is an infinite set'' is a statement.

$\left(p-q\right)+r=p-\left(q+r\right)$, $\forall p,q,r\in \mathrm{Q}$

$\left(a+b\right)+c=a+\left(b+c\right)$, $\forall a,b,c\in \mathrm{N}$

$3n+1>4$, where $n$ is a natural number.

$x^2\ge 0$ for a real number $x$.

Square numbers can be written as the sum of two odd numbers.