- Introduction to Logic
Logic is intellectual activity of reasoning. Logical Reasoning (LR) is an important topic for CAT and other aptitude based tests. Once mastered, this section provides maximum accuracy and attempt rate. Unlike quant, LR does not have much formulae to remember. Unlike Verbal, LR does not have ambiguous answers. LR is like solving puzzles simply and interestingly!
Logical Reasoning Topics
- Syllogism
Syllogism is a deductive argument having two premises and a conclusion. The question contains two premises and answer is to find the correct conclusion.
Structure
There can be any three objects or entities. The question contains two premises. Each premise and conclusion statement conains two objects. One object is common (Middle Term) in both premises. Conclusion contains two objects which are not common.
Types of Syllogism
- All (Universal Affirmatives)
- No (Universal Negatives)
- Some (Particular Affirmatives)
- Some Not (Particular Negatives)
Rules
- The middle term must not appear in the conclusion. The middle term must be distributed atleast once.
- When both premises are negative or when both premises are particular, no conclusion can be derived.
- Term which is not distributed in the premise must not be distributed in the conclusion.
- When both premises are affirmative, conclusion will be affirmative.
- If one of premises is particular, then conclusion is particular.
- If one of premises is negative, then conclusion is negative.
Examples
All animals are mortal.All men are animals.
All men are mortal.
No reptiles have fur.
All snakes are reptiles.
No snakes have fur.
All kittens are playful.
Some pets are kittens.
Some pets are playful.
No homework is fun.
Some reading is homework.
Some reading is not fun.
No healthy food is fattening.
All cakes are fattening.
No cakes are healthy food.
All horses have hooves.
No humans have hooves.
No humans are horses.
No lazy students are students who pass exams.
Some students are students who pass exams.
Some students are not lazy students.
All informative things are useful things.
Some websites are not useful things.
Some websites are not informative.
All fruit is nutritious.
All fruit is tasty.
Some tasty things are nutritious.
Some mugs are beautiful.
All mugs are useful things.
Some useful things are beautiful.
All the industrious boys in this school have red hair.
Some of the industrious boys in this school are boarders.
Some boarders in this school have red hair.
No jug in this cupboard is new.
All jugs in this cupboard are cracked.
Some of the cracked items in this cupboard are not new.
Some cats have no tails.
All cats are mammals.
Some mammals have no tails.
No tree is edible.
Some trees are green things.
Some green things are not edible.
All apples in my garden are wholesome fruit.
All wholesome fruit is ripe fruit.
Some ripe fruit are apples in my garden.
All coloured flowers are scented flowers.
No scented flowers are grown indoors.
No flowers grown indoors are coloured flowers.
- Logical Connectives
A Logical Connective (also called a logical operator) is a symbol or a word which is used to connect two or more sentences. Each logical connective can be expressed as a truth function.
Logical connectives
- NOT (Negation)
- AND (Conjunction)
- OR (Disjunction)
- IF-THEN (Material Implication)
- Seating Arrangement
Seating Arrangement questions involve arrangement of persons in a circular table, rectangular table or linear arrangement with some given conditions. In order to solve these type of questions, best strategy is to develop a rough pictorial diagram. Once diagram is complete, questions that follow can be answered in no time.
Example 1
6 Boys are sitting in a circle and facing towards the centre of the circle. Rajeev is sitting to the right ofMohan, but he is not just at the left of Vijay. Suresh is between Babu and Vijay. Ajay is sitting to the left ofVijay.
Example 2
Eleven students A, B, C, D, E, F, G, H, I, J and K are sitting in first line facing to the teacher. D who is just to the left of F, is to the right of C at second place. A is second to the right of E who is at one end. J is the nearest neighbour of A and B and is to the left of G at third place. H is next to D to the right and is at the third place to the right of I.
Example 3
Siva, Sathish, Amar and Praveen are playing cards. Amar isto the right of Sathish, who is to the right of Siva.
- Blood Relations
Brother: Mother's or father's son
Sister: Mother's or father's daughter
Uncle: Mother's or father's brother
Aunt: Mother's or father's sister
Grandfather: Mother's or father's father
Grandmother: Mother's or father's mother
Nephew: Brother's son
Niece: Brother's daughter
Cousin: Uncle or aunt's son or daughter
Brother-in-Law: Sister's husband
Sister-in-Law: Brother's wife
Daughter-in-Law: Son's wife
Son-in-Law: Daughter's husband
Sister-in-Law: Husband's or wife's sister
Brother-in-Law: Husband's or wife's brother
- Cubes
A cube is a three-dimensional solid object bounded by six faces or sides, with three meeting at each vertex.
In a cube - length, breadth and height are same while in a cuboid these are different.
If a is the side length of cube, then its volume = a3
- Clocks
The Concept
The face or dial of a watch is a circle whose circumference is divided into 60 equal part called minute spaces. A clock has two hands - the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
- In every 60 minutes, the minute hand gains 55 minutes on the hour hand.
- In every hour, both the hands coincide once, i.e 0 degrees.
- The hands are in the same straight line when they are coincident or opposite to each other. i.e 0 degrees or 180 degrees.
- When the two hands are at right angles, they are 15 minute spaces apart, i.e 90 degrees.
- When the hands are in the opposite directions, they are 30 minute spaces apart, i.e 180 degrees.
- Angle traced by hour hand in 12 hrs = 360 degrees
- Angle traced by minute hand in 60 min = 360 degrees
- If a watch or a clock indicated 8.15, when the correct time is 8, it is said to be 15 minutes too fast. On the other hand if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes slow.
- 60 min is 360 degrees, so 1 min is 60 degrees.
- The hands of a clock coincide in a day or 24 hours is 22 times, in 12 hours 11 minutes.
- The hands of clock are straight in a day is 44 times.
- The hands of a clock at right angle in a day is 44 times.
- The hands of a clock in straight line but opposite in direction is 22 times per day,
- Calendars
Odd Days
The number of days more than the complete number of weeks in a given period is number of odd days during that period.
Leap Year
Every year which is divisible by 4 is called a leap year. Thus each one of the year 1992, 1996, 2004, 2008, 2012, etc. is a leap year.
Every 4th century is a leap year but no other century is a leap year. Thus each one of 400, 800, 1200, 1600, 2000, etc. is a leap year. None of the 1900, 2010, 2020, 2100, etc. is a leap year. A leap year has 366 days.
Ordinary Year
An year which is not a leap year is called ordinary year. An ordinary year has 365 days.
Counting of odd days
One ordinary year = 365 days = 52 weeks + 1 day. Therefore, an ordinary year has 1 odd day.
One leap year = 366 days = 52 weeks + 2 days. Therefore, a leap year has 2 Odd days.
100 years = 76 ordinary years + 24 leap years = 5217 weeks + 5 days. Therefore, 100 years contain 5 odd days.
200 years contain 10 (1 week + 3 days), i.e 3 odd days.
300 years contain 15 (2 weeks +1 day), i.e 1 odd day
400 years contain (20 + 1), i.e 3 weeks, so 0 odd days. Similarly, each one of 800, 1200, 1600, etc. contains 0 odd days.
Note: (7n + m) odd days, where m less than or equal to 7 is equivalent to m odd days.
Week
Month
