(Solved): Role of counter-example & Generality True or False: The set of real numbers is closed under the ...

Role of counter-example & Generality True or False: The set of real numbers is closed under the four basic arithmetic operations. Use this problem to cite the use and power of counter-examples in mathematics. Create a false mathematical statement in the above context and provide three counter-examples (specific-gives no logic but just one counterexample, semi-general-gives some logic for falsity leading to a sub-set of counterexamples and general- gives complete logic behind falsity which leads to full set of counterexamples.)