A P Prabhakaran Solutions for Chapter: Mathematical Reasoning, Exercise 2: SELF EVALUATION TEST

Write the negation of the following statement:

Sania plays tennis.

For each of the following compound statements first identify the connecting words and
then break into component statements.

The square of an integer is positive or negative.

For the following compound statement first identify the connecting word and then break into component statements.

$x=2$ and $x=3$ are the roots of the equation $x^2$$- 5x + 6 = 0.$

Prove that the statement: "If $x, y\in Z$ such that $xy$ is odd, then both $x$ and $y$ are odd" by taking contrapositive.

For the following statement determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

Students can take French or Sanskrit as the third language.

For the following statement determine whether an inclusive "OR" or exclusive
"OR" is used. Give reasons for your answer.

Two lines intersect at a point or are parallel.

Check the validity of the statement given below by the method of contradiction.
$p :$The sum of an irrational number and a rational number is irrational"

Find the component statement of the following and check whether they are true or
not.
"All prime numbers are either even or odd".