Let S be the statement: The product of any irrational number and any nonzero rational number is irrational. (a) Write a negation for S. (b) Prove S by contradiction.

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 be an irrational number and be a rational number.

where is rational.

So,

As quotient of two rational numbers is also rational, must be rational which is a contradiction to the fact that is irrational.

Yes it is

Step-by-step explanation:

when you add up all parts of a triangle they are equal to 180