Answer:
The proposed negation is not correct. A possible corect negation woulld be: There is an irrational number and, a rational number whose product is rational.
Step-by-step explanation:
From the given information above:
STATEMENT: "The product of <em>ANY</em> irrational number and <em>ANY </em>rational number is irrational".
From the above statement, the word <em>"ANY"</em> is very vital. Let assume we choose an element x from a particular set X of irrational numbers, as well as an element y from the set Y of a rational number, therefore, the statement has a use case and applies to every x and y element. Thus, in an effective mathematical way, the statement typically implies "for all x in set X and for all y in set Y, the product x*y is irrational.
However; from the negation of the "for all" statement is "there exists" (any text in discrete arithmetic will assist you to become fully aware of this fact). Any ramifications in the statement is likewise negated, i.e; if the statement infers that the resulted product of x and y is irrational, at that point the negation(invalidation) infers that the item isn't irrational. For example, it is rational. At the point when we set up every one of these facts, we get:
"There exist an element x in the set X, in addition to that; there exists an element y in set Y; x*y is rational".
If we express that into the option given; the right option is:
"There exist an irrational number and a rational number whose product is rational"
