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Monday, June 6, 2016
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Wednesday, May 25, 2016
Introduction to Logic in Reasoning
Introduction to Logic in Reasoning
How do we know that tomorrow sun rises in the east? How do we know that if we touch the fire it burns us? Eventhough there are scientifiic proves, mostly we argue based on our past experiences.
Let us take one example:
Proposition: Mr.X is driving a rolls royce car
Conclusion: so Mr.X is a rich person
You might argue that this argument is not valid because Mr.X can be driver or the car or may be it is a rented car. But If you are living in a developed country where Rolls Royce cars can be seen every where, you are most likely to agree that Mr.X is a rich person as he is driving the Rolls royce.
This reasoning is called Inductive reasoning or probability. This reasoning is proposed by David Hume. He suggested that the people who won't agree with this type of reasoning must be starved to death as this is one of the most important way of convincing people and to draw valid conclusions.
Let us take another Argument:
Proposition: Sachin is a great batman
Conclusion: So India will win the match
Some of you again may not agree with the varacity of the conclusion but If I may add another proposition "Great batsman help teams to win matches" then this argument looks like below
Proposition: Sachin is a great batman
Proposition: Great batsman help teams to win matches
Conclusion: So India will win the match
Now this is more convincing. This type of reasoning is called Deductive reasoning. This is proposed by Aristotle. He studied 216 different structures of Deductive reasoning and found that only 16 structures give valid conclusions.
Let us look at a couple of the false arguments
1. Propositions are valid but conclusion is false
Proposition: If Bills gates has kohinoor diamond then He is rich
Proposition: Bill Gates does not have Kohinoor
Conclusion: So he is not rich
We know this is a false conclusion, even though both the propositions are true
2. Propositions are false but conclusion is true
Proposition: All Rats are CATs
Proposition: All CAT are Dogs
Conclusion: All Rats are Dogs
Clearly both the propositions are false but given the propositions true, the conclusion is true.
We will see lot of arguments in our daily life. These arguments range from convincing our friend to make him watch your favorite hero movie to whether Bihar state has to be given or not. Critical reasoning is the use of logic to evaluate arguments.
Logic is defined as the study of methods and principles used to distinguish good (correct) reasoning from bad (incorrect) reasoning. Let us have a look at some technical terms
Argument:
An argument is a group of statements (propositions) where the statements follow one another and ultimately give a final statement known as the conclusion or inference. The group of all these statements including the conclusion is known as an argument.
Most questions in Logical reasoning are based on whether the student is capable of testing the validity of an Argument, the first thing one has to clearly understand is the concept of the Argument. For the purposes of understanding the concept of the Argument fully, it would help to get acquainted with a few key terms.
Elements of an Argument:
Proposition: A proposition is the basic units of an argument. A typical proposition has a relationship spelled out between a subject and an object in the form a sentence.
Illustration: of Proposition
Eg: All Andhrites are Indians
Here “Andhrites is the subject and “Indians” is predicate
Premise: The term premise is applied to the proposition that gives rise to the conclusion or the inference. Unless the premise is valid, the conclusion will not be valid.
Conclusion or inference: The conclusion or inference of an argument is the final proposition that is affirmed on the basis of other propositions of the same argument.
Argument = Proposition 1 (Premise) + Proposition 2 (Premise) + Proposition 3 (Conclusion)
Eg: All Students are good
Rama is a student
Rama is good
Types of arguments:
Deductive argument: A deductive argument is one whose conclusion is claimed to follow from its premises with absolute necessity or certainty, this certainty not being a matter of degree and not depending in any way on anything else. Therefore a deductive argument has to be either valid or invalid. There is no grey area in between.
In competitive exams questions on this area comes under the header "syllogisms or Statements and conclusions"
Inductive Argument: An inductive argument is one whose conclusion is claimed to follow from its premises only with probability, Inductive arguments, therefore, cannot be absolutely valid or invalid, the way deductive arguments are. But most of the arguments we make in our life are based on inductive reasoning. We may not convince others purely based on deduction, but by giving some past examples.
In most of the competitive exams questions on this area comes under the header "Critical reasoning".
Let us take one example:
Proposition: Mr.X is driving a rolls royce car
Conclusion: so Mr.X is a rich person
You might argue that this argument is not valid because Mr.X can be driver or the car or may be it is a rented car. But If you are living in a developed country where Rolls Royce cars can be seen every where, you are most likely to agree that Mr.X is a rich person as he is driving the Rolls royce.
This reasoning is called Inductive reasoning or probability. This reasoning is proposed by David Hume. He suggested that the people who won't agree with this type of reasoning must be starved to death as this is one of the most important way of convincing people and to draw valid conclusions.
Let us take another Argument:
Proposition: Sachin is a great batman
Conclusion: So India will win the match
Some of you again may not agree with the varacity of the conclusion but If I may add another proposition "Great batsman help teams to win matches" then this argument looks like below
Proposition: Sachin is a great batman
Proposition: Great batsman help teams to win matches
Conclusion: So India will win the match
Now this is more convincing. This type of reasoning is called Deductive reasoning. This is proposed by Aristotle. He studied 216 different structures of Deductive reasoning and found that only 16 structures give valid conclusions.
Let us look at a couple of the false arguments
1. Propositions are valid but conclusion is false
Proposition: If Bills gates has kohinoor diamond then He is rich
Proposition: Bill Gates does not have Kohinoor
Conclusion: So he is not rich
We know this is a false conclusion, even though both the propositions are true
2. Propositions are false but conclusion is true
Proposition: All Rats are CATs
Proposition: All CAT are Dogs
Conclusion: All Rats are Dogs
Clearly both the propositions are false but given the propositions true, the conclusion is true.
We will see lot of arguments in our daily life. These arguments range from convincing our friend to make him watch your favorite hero movie to whether Bihar state has to be given or not. Critical reasoning is the use of logic to evaluate arguments.
Logic is defined as the study of methods and principles used to distinguish good (correct) reasoning from bad (incorrect) reasoning. Let us have a look at some technical terms
Argument:
An argument is a group of statements (propositions) where the statements follow one another and ultimately give a final statement known as the conclusion or inference. The group of all these statements including the conclusion is known as an argument.
Most questions in Logical reasoning are based on whether the student is capable of testing the validity of an Argument, the first thing one has to clearly understand is the concept of the Argument. For the purposes of understanding the concept of the Argument fully, it would help to get acquainted with a few key terms.
Elements of an Argument:
Proposition: A proposition is the basic units of an argument. A typical proposition has a relationship spelled out between a subject and an object in the form a sentence.
Illustration: of Proposition
Eg: All Andhrites are Indians
Here “Andhrites is the subject and “Indians” is predicate
Premise: The term premise is applied to the proposition that gives rise to the conclusion or the inference. Unless the premise is valid, the conclusion will not be valid.
Conclusion or inference: The conclusion or inference of an argument is the final proposition that is affirmed on the basis of other propositions of the same argument.
Argument = Proposition 1 (Premise) + Proposition 2 (Premise) + Proposition 3 (Conclusion)
Eg: All Students are good
Rama is a student
Rama is good
Types of arguments:
Deductive argument: A deductive argument is one whose conclusion is claimed to follow from its premises with absolute necessity or certainty, this certainty not being a matter of degree and not depending in any way on anything else. Therefore a deductive argument has to be either valid or invalid. There is no grey area in between.
In competitive exams questions on this area comes under the header "syllogisms or Statements and conclusions"
Inductive Argument: An inductive argument is one whose conclusion is claimed to follow from its premises only with probability, Inductive arguments, therefore, cannot be absolutely valid or invalid, the way deductive arguments are. But most of the arguments we make in our life are based on inductive reasoning. We may not convince others purely based on deduction, but by giving some past examples.
In most of the competitive exams questions on this area comes under the header "Critical reasoning".
Monday, May 23, 2016
Non-Verbal Reasoning (Analogy) Interview questions
Non-Verbal Reasoning (Analogy) Interview questions
Analogy means relationship. Let us have a look at an example:
Teacher : Pen : : Soldier : _________
What should come in the blank? If teacher's main tool is pen, Soldier's main tool is a gun.
Similarly, we have to identify the relationship between in figures A and B so that to identify the option which got relationship with figure C.
Just look at few examples and you can easily understand these problems:
1.
The square in PF(A) rotated 90$^0$ clockwise along with dot. So option 5 is correct.
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Here the hexagon becae pentagon and the dots came out of the diagram, and a new darkened dot appeared in the middle. So PF(C) should become triangle and two dots must come out and a darkened dot must appear in the iddle. So correct Option 5
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Questions for Practice
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Saturday, May 21, 2016
Amcat-previous-papers
Amcat-previous-papers
- Amcat previous questions set - 5
- Amcat previous questions set - 4
- Amcat previous questions set - 3
- Amcat previous questions set - 2
- Amcat previous questions set - 1
More sets are coming up...
Non - verbal reasoning (Series)Interview questions
Non - verbal reasoning (Series)Interview questions
Non-Verbal reasoning appears in Bank exams, Infosys, MAT exams constantly. There are 5 Problem Figures (PF) will be given with 5 Answer Figures (AF). We need to determine the next figure in the series. There are certain rules which make solving these problems easy. So study the rules and solved examples.
2.
Here PF(C) and PF(E) are equal. So Answer figure should be PF(B). So correct option is c.
3.
The arrow is changing its positions clock wise 90o, 45o, 135o, 45o, ....next should be 180o. So option 3.
4.
Simple one. A new arrow and a new line are adding alternatively. In PF(E) a new line has added. So in the next figure a new arrow must be added. And total lines should be 6. Option 5
5.
Small hand is moving anticlock wise 90o, 45o, 90o, 45o,... and Big hand is moving clock wise 135o constantly. So in the next figure, small hand must move 90o anti clockwise, and big hand must move 135o. So option 4
6.
Here the symbol is changing positions anti clockwise by 45o and every time a new symbol is adding. The "C"s in the middle are rotating clock wise by 90o. So the next figure must be option 4
7.
This is a simple analogy. There is a relationship between 1 and 2, 3 and 4. the small figures in the first diagram are getting bigger and vice-versa. So Option 3
8.
All the three symbols in the dice are rotating clockwise. So option 3
Alternative method:
We know that if PF(A) = PF(D), PF(B) = PF(E) then answer is PF(C). So option 3
9.
A new symbols is appearing in the middle of the previous figure and the previous figure is getting bigger. So option 4 is the right option. 3 and 5 options are ruled out as the figures in the middle are appeared already.
10.
A dot and line are adding constantly to the figures in left and right sides alternatively. So option 3
11.
There appears to be no pattern on immediate look, but his problem can be solved by simple observation. Have a look at the diagram below..
The positions of two symbols are not changing in 2 consecutive figures. So option 5
12.
the arrow and small line inside the small square are rotating constantly anti clockwise and clockwise respectively by 90o, 45o, 90o, 45o,... and 45o, 90o, 45o, 90o . So next figure would be option 3.
13.
The line is rotating anti clock wise by 90o, 180o, 270o, 360o so next figure should be 90o from figure E and a new symbol must appear. So option 1 is the correct.
14.
Symbols X is rotating clockwise by 45o, 90o, 45o, 90o. So our options will be either 1 or 3 as in the next figure symbol X must move 45o. A new symbols is being added to X each time one at front and next time at back. So option 3 is right one.
15.
Simple. Observe PF(A) and PF(E) are equal. So next figure will be PF(B). So option 5
16.
the symbols are changing constantly in clockwise direction and a new symbol is being added.
The red rounded circle is a place whenever a symbol appear in that position must not appear in the next. And remaining positions are moving clockwise by 90o. A new symbol must come at the place shown by green arrow. So our option will be 1. Option 2 is ruled out as + symbol appeared earlier.
17.
Circle is moving diagonally and triangle is moving clockwise by 90o. So option 1 is correct one.
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19.
Simple one. Figures A and B changed their symbols opposite them. C and D also did So. So option 1
20.
Symbols in A, B are same except Symbols at bottom. A new symbol is coming there. Similarly in C, D. So option 3. Option 2 is ruled out as C appeared earlier.
How to answer these questions:
Step 1:
For all the series problems the following rules apply. If problem figures A and E are equal our answer is problem figure B. Similarly, the other rules as follows.
1. PF(A) = PF(E) then answer is PF(B)
2. PF(D) = PF(E) then answer is PF(C)
3. PF(A) = PF(C) = PF(E) then answer is PF(B)
4. PF(A) = PF(D), PF(B) = PF(E) then answer is PF(C)
5. PF(D) = inverse of PF(A) and PF(E) = inverse of PF(2) then answer is inverse of PF(C)
Step 2:
In general, the items in the box takes different positions in the subsequent figures. They may rotate certain degrees either clock wise or anti-clockwise. Look at the following diagram. In some problems new items add to the existing figures and some existing figures vanish.
Solved Examples
1.
In this problem If PF(A) = PF(E) then answer is PF(B). In the answer options AF(4) is same as PF(B) so option 4
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Alternative method:
We know that if PF(A) = PF(D), PF(B) = PF(E) then answer is PF(C). So option 3
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There appears to be no pattern on immediate look, but his problem can be solved by simple observation. Have a look at the diagram below..
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Here you can easily observe that the lines are rotating 90o clockwise. also in PF(B) and PF(D), half line has added at the right most side and in figures PF(C) and PF(E) a new line has added. So in our answer half line has to be added and lines should rotate 90o. So answer option 2.
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