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.

Question

Philoid · Accepted Answer

Negation of statement p is 'not p.' The negation of p is symbolized by '~p.' The truth value of ~p is the opposite of the truth value of p.

The negation of the statement:

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

is

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

So, the given statement is not the negation of the first statement.

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.