Tag: proof by contradiction

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Questions Related to proof by contradiction

Multiple choice mathematical modelling proof by contradiction similar triangles

To understand objects that are too small or too large to see,

  1. physical model is used

  2. mathematical model is used

  3. conceptual model is used

  4. mechanical model is used
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In order to see too small objects , we use microscope 

We might use Physical model to see the microscopic cells as well as the large cells
Therefore option $A$ is correct

Multiple choice mathematical modelling proof by contradiction similar triangles

State the following statement is True or False
The terms  $(x+y)^2$ and $x^2$ + $ y^2$  are equivalent.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The statement is False as ${ \left( x+y \right)  }^{ 2 }={ x }^{ 2 }+{ y }^{ 2 }+2xy$ which is not equivalent to ${ x }^{ 2 }+{ y }^{ 2 }$.

Multiple choice mathematical modelling proof by contradiction similar triangles

Scientists who study universe are known as

  1. Astrologers

  2. Astronomers

  3. Geologists

  4. Meteorologists
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A: Astrologers $\rightarrow$ People who study of stars and other celestial objects.

B: Astronomers $\rightarrow$ People who study the universe.
C: Geologists $\rightarrow$ People who studies the solid and liquid matter that constitute the earth as well as the processes that shape it.
D: Meteorologists $\rightarrow$  People who study atmosphere. 



Multiple choice mathematical modelling proof by contradiction similar triangles

Scientists use models to help guide their search for

  1. life on earth

  2. existence of living organisms

  3. other worlds

  4. new information
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Scientists use models to help them get new information and use these information in their research.

Multiple choice mathematical modelling proof by contradiction similar triangles

The contradiction of the statement to prove by contradiction method of the following will be
" If function is continuous then it is differentiable."

  1. Assume function is differentiable.

  2. Assume function is not continuous.

  3. Assume function is continuous.

  4. Assume function is not differentiable.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To prove an implication by contradiction, we need to assume the inverse of its conclusion and them show that our assumption is wrong.

Hence $D$ is correct

Multiple choice mathematical modelling proof by contradiction similar triangles

Which of the following is the correct steps to take when proving a statement using proof by contradiction?

  1. 1) Assume that your statement is true.

    2) Show this is the case using definitions and theorems.

    3) State that the statement is true.

  2. 1) Assume your statement is true for a certain instance.

    2) Show that it is true in more than one instance.

    3) State that your statement must be true.

  3. 1) Assume your statement to be false.

    2) Proceed as you would in a direct proof.

    3) Come across a contradiction.

    4) Use the contradiction to state that your assumption of the statement being false can't be the case, so your statement must be true.

  4. None of the answers are correct.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Proof by contradiction can be used to prove any kind of statements.

Steps to be followed:
     $\rightarrow$ Assume the statement we want to prove to be false.
     $\rightarrow$ Then start proving from that statement. 
     $\rightarrow$ We end up seeing our assumption to be wrong.
     $\rightarrow$ Now we can conclude our statement to be true. 

Multiple choice mathematical modelling proof by contradiction similar triangles

Scientists who study earth's atmosphere have developed

  1. physical climate models

  2. conceptual climate models

  3. mathematical climate models

  4. aerial climate models
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Scientists who study about atmosphere develop mathematical climate models which depict longitudinal and latitudinal measures and area covered by a region.

Multiple choice mathematical modelling proof by contradiction similar triangles

A pattern, plan, representation or description designed to show structure is known as a

  1. sample

  2. model

  3. design

  4. structure
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sample: It is a small amount of an element or a compound.

Model: A 3D plan or representation, designed to show structure.
Design: Pictorial representation of a structure.
Structure: An arrangement of the relations between the parts or elements of something complex.

So, the correct answer is "Model".

Multiple choice mathematical modelling proof by contradiction similar triangles

The contrapositve of the statement If Mohan works hard, then he gets a first class is

  1. If Mohan gets first class, then he does not works hard

  2. If Mohan does not get a first class, then he works hard

  3. If Mohan does not get a first class, then he does not work hard

  4. If Mohan does not work hard, then he does not get a first class
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice mathematical modelling proof by contradiction similar triangles

To prove : "The integers can be of the form $4n,4n+1,4n+2  \ or \ 4n+3$" by direct method, we shall start the proof by the assumption 

  1. Let integers not of form $4n,4n+1,4n+2 \ or \ 4n+3$.
  2. Let integers be not of form $4n$.
  3. Let $z$ be any integer.
  4. Let $z<0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As we are solving by direct method we need to assume what is given in the hypothesis, which is in this case z be any integer.

$C$