Check whether the following pair of statements are negation of each other. Given reasons for your answer: `a+b=b+a` is true for every real number `a\ a n d\ bdot` There exist real numbers `a\ a n d\ b` for which `a+b=b+adot`

Check whether the following pair of statements are 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 exists real numbers x and y for which x + y = y + x

State, whether the following statements are true of false. a - c gt b -d , then a + d gt b + c

p : xy =yx , is true for every real number x and y q : There exists real number x and y for which xy=yx is not true. above pair of statement are

Which of the following statements are true? Give reason to support your answer. {a , b , a , b , a , b dot} is an infinite set.

State, whether the following statements are true of false. If a lt b, and c gt 0 , then a - c gt b - c where a, b, c and d are real number and c =! 0 .

Write the negation of the following statements and check whether the resulting statements are true: Every natural number is greater than 0.

If a and b are real numbers, with a gtb and |a| lt|b| , then

Find the geometric means of the following pairs of number: a^3b\ a n d\ a b^3dot

State whether the following statements are true or false. Justify your answers, (i) Every irrational number is a real number.(ii) Every point on the number line is of the form sqrt(m) , where m is a natural number.(iii) Every real number is an irrational number.

Write which of the following statements are true? Justify your answer: The sets P={a}a n d\ B={{a}} are equal.