Q: Find a counterexample to the statement all us presidents have served only one term to show that this statement is false.?

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That is a false statement... o.O

That is a false statement. The President is part of the executive branch.

The government does not sponsor clinical trials

We don’t have your list of statements so can’t provide an answer.

He supported the british monarchy in its struggle to limit the rights of people

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A counterexample is a specific case in which a statement is false.

Counterexample

an example of this is like taking a statement and making it negative, i think.... Such as, "All animals living in the ocean are fish." A counterexample would be a whale(mammal), proving this statement false.

The statement is not false. A hexagon is a polygon.

A counterexample is an example (usually of a number) that disproves a statement. When seeking to prove or disprove something, if a counter example is found then the statement is not true over all cases. Here's a basic and rather trivial example. I could say "There is no number greater than one million". Then you could say, "No! Take 1000001 for example". Because that one number is greater than one million my statement is false, and in that case 1000001 serves as a counterexample. In any situation, an example of why something fails is called a counterexample.

Yes.

It's a counterexample.

That is false. This type of statement is only true for prime numbers, not for compound numbers such as 6. Counterexample: 2 x 3 = 6

A trapezium.

The use of Counterexamples. Counterexample - is an exception to a proposed general rule. For example, consider the proposition "all students are lazy". Because this statement makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false. Thus, any hard-working student is a counterexample to "all students are lazy". More precisely, a counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement).

A counterexample. For example, somebody could say that the empire state building is 1 ft tall, and a counterexample would be the empire state building is taller than the space needle and the space needle is over 500', therefore the empire state building is not 1 ft tall, or whatever.

No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:x = 3 if and only if x2 = 9.From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):The Conditional Statement: If x = 3 then x2 = 9.This statement is true. However, the second statement we can extract is called the converse.The Converse: If x2=9 then x = 3.This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.All it takes to prove that a statement is false is one counterexample.