State whether the given statement is true or false. Justify your answer.

All prime numbers are odd.

State whether the given statement is true or false. Justify your answer.

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

State whether the given statement is true or false. Justify your answer.

$x^2>0$, where $x$ is a real number.

State whether the given statement is true or false. Justify your answer.

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

State whether the given statement is true or false. Justify your answer.

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

State whether the given statement is true or false. Justify your answer.

$\left(x+y\right)-z=x+\left(y-z\right)$, $\forall x,y,z\in \mathrm{ℝ}$

Some axiom, theorem and definitions are given. Read carefully.

$1.$ Whole is greater than part. $($Axiom$)$

$2.$ If three sides of a triangle are different in measure, then that triangle is called scalene triangle. $($Definition$)$

$3.$ If $n$ is an odd integer then it can be expressed as, $n=2k+1$, where $k$ is any integer. $($Definition$)$

$4.$ Two triangles are congruent if the three sides one triangle are equal to corresponding three sides of other triangle. $($Theorem$)$

$5.$ If two things are equal to the same third thing then they also equal to one another. $($Axiom$)$

Write possible conclusions on the basis of above statements for the following statement.

In triangles $RST$ and $XYZ$, $RS=XY$, $ST=YZ$ and $TR=ZX$.

Some axiom, theorem and definitions are given. Read carefully.

$1.$ Whole is greater than part. $($Axiom$)$

$2.$ If three sides of a triangle are different in measure, then that triangle is called scalene triangle. $($Definition$)$

$3.$ If $n$ is an odd integer then it can be expressed as, $n=2k+1$, where $k$ is any integer. $($Definition$)$

$4.$ Two triangles are congruent if the three sides one triangle are equal to corresponding three sides of other triangle. $($Theorem$)$

$5.$ If two things are equal to the same third thing then they also equal to one another. $($Axiom$)$

Write possible conclusions on the basis of above statements for the following statement.

$\frac{AB}{2}=AC$

Some axiom, theorem and definitions are given. Read carefully.

$1.$ Whole is greater than part. $($Axiom$)$

$2.$ If three sides of a triangle are different in measure, then that triangle is called scalene triangle. $($Definition$)$

$3.$ If $n$ is an odd integer then it can be expressed as, $n=2k+1$, where $k$ is any integer. $($Definition$)$

$4.$ Two triangles are congruent if the three sides one triangle are equal to corresponding three sides of other triangle. $($Theorem$)$

$5.$ If two things are equal to the same third thing then they also equal to one another. $($Axiom$)$

Write possible conclusions on the basis of above statements for the following statement.

$l=\frac{k+5}{2}$ and $2m=k+5$, where $k,l,m\in R$.