Check whether the following pair of statements is a negation of each other. Give reasons for your answer. (i) a + b = b + a is true for every real number a and b. (ii) There exist real numbers a and b for which a + b = b + a.
Check whether the following pair of statements is a negation of each other. Give reasons for your answer. (i) a + b = b + a is true for every real number a and b. (ii) There exist real numbers a and b for which a + b = b + a.

Answer:

The negation of the statement:

p: a + b = b + a is a true for every real number a and b.

~p: There exist real numbers are ‘a’ and ‘b’ for which a+b ≠ b+a.

The statement is not the negation of the first statement.