Answer:
Negation: The product of any irrational number and any nonzero rational number is not irrational.
Step-by-step explanation:
(a)
Given statement: The product of any irrational number and any nonzero rational number is irrational.
Negation: The product of any irrational number and any nonzero rational number is not irrational.
(b)
Let if possible the product of any irrational number and any nonzero rational number is not irrational that is rational.
Let [tex]x[/tex] be an irrational number and [tex]y\neq 0[/tex] be a rational number.
[tex]xy=z[/tex] where [tex]z[/tex] is rational.
So,
[tex]xy=z\\x=\frac{z}{y}[/tex]
As quotient of two rational numbers is also rational, [tex]x[/tex] must be rational which is a contradiction to the fact that [tex]x[/tex] is irrational.
