# What is an example of a counterexample?

## What is an example of a counterexample?

For example, the fact that “John Smith is not a lazy student” is a counterexample to the generalization “students are lazy”, and both are counterexample to, and disproof of, the generalization “all students are lazy.”

What is a counter example geometry?

A counterexample is an example in which the hypothesis is true, but the conclusion is false. If you can find a counterexample to a conditional statement, then that conditional statement is false.

How do you write a counter example in geometry?

To give a counterexample, I have to find an integer n such n2 is divisible by 4, but n is not divisible by 4 — the “if” part must be true, but the “then” part must be false. Consider n = 6. Then n2 = 36 is divisible by 4, but n = 6 is not divisible by 4. Thus, n = 6 is a counterexample to the statement.

### Which is a counterexample of any number divisible by 2 is divisible by 4?

∴ , 14 is the counterexample for the 2nd statement that states “If a number is divisible by 2, it is also divisible by 4.”

Can a theorem have counterexamples?

A theorem is based on deductive reasoning and cannot have counterexamples. A theorem is a conclusion that has been proven to be true by deductive reasoning. Deductive reasoning is not based on​ observations; therefore, a conclusion made using deductive reasoning is absolutely certain and cannot have counterexamples.

Are counterexamples always sometimes or never true?

Examples (statement true): Counterexamples (statement false):…

The truthfulness of logical statements
A statement is: if:
Sometimes true There is at least one example and at least one counterexample
Never true There are no examples, only counterexamples

#### Are counterexamples always true?

Counterexamples are used to prove that a statement is invalid. Identify the hypothesis and the conclusion in the given statement. The counterexample must be true for the hypothesis but false for the conclusion.

What is a counterexample in fractions?

counterexample. A counterexample is an example that disproves a conjecture. fraction. A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar.

What is the counterexample principle?

The Counterexample Principle: Since a mathematical statement is true only when it is true 100 percent of the time, we can prove that it is false by finding a single example where it is not true.

## Is a counterexample proof?

A proof by counterexample is not technically a proof. It is merely a way of showing that a given statement cannot possibly be correct by showing an instance that contradicts a universal statement.

Is counter example one word?

an example that refutes an assertion or claim.

What is counterexample in set theory?

Counterexamples around cardinality (part 1) We denote by |A| the cardinality of the set A. We say that A and B have the same cardinality if there exists a bijection from A onto B. Such sets said to be equinumerous. The finite sets satisfy the property that if A⊂B and A and B have the same cardinality then A=B.

### What is a counter example in a truth table?

A counterexample to an argument is a case in which the premises are true and the conclusion is false.

How do you use counterexample in a sentence?

Counterexample in a Sentence 1. The math teacher provided a counterexample to prove to the student that her solution was incorrect. 2. By providing a counterexample, the scientist was able to convince his colleague that his initial theory was invalid.

What is counterexample reasoning?

Definition: A counter-example to an argument is a situation which shows that the argument can have true premises and a false conclusion.

#### How many counter examples are needed to prove that a statement is false Why?

Answer and Explanation: A counterexample is used to prove a statement to be false. So to prove a statement to be false, only one counterexample is sufficient.

Which one is a counter-example to disprove?

Disproof by Counter-Example Notes Not surprisingly, disproof is the opposite of proof so instead of showing that something is true, we must show that it is false. Any statement that makes inferences about a set of numbers can be disproved by finding a single example for which it does not work.

What is a counterexample in logic?

## What is logic gate in computer science?

A logic gate is a series of transistors connected together to give one or more outputs , each output being based on the input or combination of inputs supplied to it.

What is conditional proposition in discrete mathematics?

The conditional statement P→Q means that Q is true whenever P is true. It says nothing about the truth value of Q when P is false. Using this as a guide, we define the conditional statement P→Q to be false only when P is true and Q is false, that is, only when the hypothesis is true and the conclusion is false.

What is counterexample explain how counter example helps in problem solving?

Counterexample is an example with a negative connotation. Whereas an example may be used to support or illustrate a claim, a counterexample is used to refute an assertion. How an example is being used often depends on the purpose or the formulation.

### What is circuit in digital electronics?

Digital circuit: A digital circuit is a circuit where the signal must be one of two discrete levels. Each level is interpreted as one of two different states (for example, on/off, 0/1, true/false). Digital circuits use transistors to create logic gates in order to perform Boolean logic.

What is digital logic design?

Digital logic design is a system in electrical and computer engineering that uses simple number values to produce input and output operations. As a digital design engineer, you may assist in developing cell phones, computers, and related personal electronic devices.

What type of statement is Q ↔ ∼ P?

Disjunction statements are compound statements made up of two or more statements and are true when one of the component propositions is true….Disjunction.

p q p∨q
T F T
F T T
F F F

#### What is logic circuit in computer?

logic circuit. noun. an electronic circuit used in computers to perform a logical operation on its two or more input signals. There are six basic circuits, the AND, NOT, NAND, OR, NOR, and exclusive OR circuits, which can be combined into more complex circuits.

What is logic gates in digital electronics?

A logic gate is a device that acts as a building block for digital circuits. They perform basic logical functions that are fundamental to digital circuits. Most electronic devices we use today will have some form of logic gates in them.