Mathematical Statements

Prove that $8n + 7$ is an odd integer, where $n$ is an integer.

Write the converse and contrapositive of the statement "If you do not obey traffic rules, then there will be a traffic jam".

Explain the value reflected in the statement.

Give the answer on the basis of instructions for the mathematical statement.

$x^2=1 \Rightarrow x=1$

Write this statement in the form of 'if-then'.

Is this statement true?

Is statement true if when $x\in N$?

Prove the following theorem.

If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Identify the steps in proof by contradiction

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 $x+y=y+x$.

$10+2=12$ is a mathematically acceptable statement.

• $9+2=11$ is a mathematically acceptable statement.

What is the difference between a mathematically acceptable statement and a mathematically unacceptable statement? 

In the method of proofs by contradiction, we assume that the contradictory statement of the given statement is false, and we are logically trying to prove that assumption is true.

Identify the step in proof by contradiction

In the method of proofs by contradiction, we assume that the contradictory statement of the given statement is true, and we are logically trying to prove that assumption is wrong.

Identify the steps in proof by contradiction

What are the steps to be followed in proof by contradiction?

What is the method of mathematical proofs by contradiction? 

For each real number$x$, if  $0<x<1$, then $\frac{1}{x\left(1-x\right)}⩾4$

Prove that there exist no integers $a$ and $b$ for which $18a+6b=1$

Prove $\sqrt{2}$ is irrational.

State whether the statement is True or false. Justify the statement.

For all integers $n$, if $n^3+5$ is odd, then $n$ is even. 

Identify whether the given statement "The whole is greater than a part" is a conjecture, axiom or theorem.