MTH202 Solved Subjective Final term Exam

Question: What is a combination?

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Answer: A combination is an un-ordered collection of unique

elements. Given S, the set of all possible unique

elements, a combination is a subset of the elements of

S. The order of the elements in a combination is not

important (two lists with the same elements in

different orders are considered to be the same

combination). Also, the elements cannot be repeated in

a combination (every element appears uniquely once

Question: why is 0! equal to 1?

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Answer: Since n! = n(n-1)!

Put n =1 in it.

1! = 1x(1 – 1)!

1! =1x0!

1! = 0!

Since 1! = 1

So 1 = 0!

0! = 1.

Question: What is the basic idea if Mathematical Induction?

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Answer: Mathematical Induction

Question: Define symmetric and anti-symmetric.

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Question: What is the main deffernce between Calculus and

Discrete Maths?

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Answer: Discrete mathematics is the study of mathematics

which concerns to the study of discrete objects.

Discrete math build students approach to think

abstractly and how to handle mathematical models

problems in computer While Calculus is a mathematical

tool used to analyze changes in physical quantities. Or

"Calculus is sometimes described as the mathematics

of change." Also calculus played an important role in

industrial area as well discrete math in computer.

Discrete mathematics concerns processes that consist

of a sequence of individual steps. This distinguishes it

from calculus, which studies continuously changing

processes. the ideas of discrete mathematics

underline the science and technology specific to the

computer age. An important goal of discrete

mathematics is to develop students’ ability to think

abstractly.

Question: Explain Valid Arguments.

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Answer: When some statement is said on the basis of a

set of other statements, meaning that this statement

is derived from that set of statements, this is called

an argument. The formal definition is “an argument is a

list of statements called “premises” (or assumptions or

hypotheses) which is followed by a statement called

the “conclusion.”

A valid argument is one in which the premises

imply the conclusion.

1) It cannot have true premises and a false

conclusion.

2) If its premises are true, its conclusion must

be true.

3) If its conclusion is false, it must have at least

one false premise.

4) All of the information in the conclusion is also

in the premises.

Question: What is the Difference between combinations and

permutations?

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Answer: When we talk of permutations and combinations in

everyday talk we often use the two terms

interchangeably. In mathematics, however, the two

each have very specific meanings, and this distinction

often causes problems

In brief, the permutation of a number of objects is

the number of different ways they can be ordered; i.e.

which one is first, which one is second or third etc. For

example, you see, if we have two digits 1 and 2, then 12

and 21 are different in meaning. So their order has its

own importance in permutation.

On the other hand, in combination, the order is not

necessary. you can put any object at first place or

second etc. For example, Suppose you have to put some

pictures on the wall, and suppose you only have two

pictures: A and B.

You could hang them

or

We could summarise permutations and combinations

(very simplistically) as

Permutations - position important (although choice may

also be important)

Combinations - chosen important,

which may help you to remember

Question: What is the use of kruskal's algorithn in our daily life?

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Answer: The Kruskal’s algorithm is usually used to find minimum

spanning tree i.e. the possible smallest tree that

contains all the vertices. The standard application is to

a problem like phone network design. Suppose, you have

a business with several offices; you want to lease

phone lines to connect them up with each other; and

the phone company charges different amounts of

money to connect different pairs of cities. You want a

set of lines that connects all your offices with a

minimum total cost. It should be a spanning tree, since

if a network isn't a tree you can always remove some

edges and save money. A less obvious application is

that the minimum spanning tree can be used to

approximately solve the traveling salesman problem. A

convenient formal way of defining this problem is to

find the shortest path that visits each point at least

once.

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Question: What is irrational number?

Answer: Irrational number An irrational number can not be

expressed as a fraction. In decimal form, irrational

numbers do not repeat in a pattern or terminate. They

"go on forever" (infinity). Examples of irrational

numbers are: pi= 3.141592654...

Question: Define membership table and truth table.

Answer: Membership table: A table displaying the membership

of elements in sets. Set identities can also be proved

using membership tables. An element is in a set, a 1 is

used and an element is not in a set, a 0 is used. Truth

table: A table displaying the truth values of

propositions.

Question: Define function and example for finding domain and

range of a function.

Answer:

Question: Why do we use konigsberg bridges problem?

Answer:

Question: Explain the intersection of two sets?

Answer:

Question: What is absurdity With example?

Answer:

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By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com