Give a counterexample to the statement “If n is an integer and n2 is divisible by 4, then n is divisible by 4.” To give a counterexample, I have to find an integer n such n2 is divisible by 4, but n is not …

We suggest the following counterexample: In order to see that these two linear functions are not perpendicular, we notice that the slop of the rst function is 3. Therefore, the slope of a perpendicular …

To make it valid, we’ll need to ADD a claim about the relationship between being a mammal and having hair. Something like: All dolphins are mammals. All mammals are things that have hair. Therefore, all …

Counterexample The function y 3p D x2 is continuous on R and the tangent line exists at any point on its graph, but the function is not differen-tiable at the point x D 0.

For instance, a polynomial as an example of a continuous function is not a counterexample, but a polynomial as an example of a function that fails to be bounded or of a function that fails to be …

Counterexample without cases J. Marshall Ash Abstract. The standard examples of functions without a one-sided limit are defined piecewise, with at least two pieces. We give an example of a function …

Disproof by counter-example: find one example for which the statement does not hold true.