Subset

So what is the basic difference between a set and a sub-set? The answer is simple. A set has all the elements that are present in  a subset but a subset. does not contain all the elements of a set, it contains only a few elements. But it crucial to note that a subset. of a particular set will have no element that is other then what is present in that set.

So a subset. is a smaller or condensed form of a set. Let us consider a set of integers less than 5 and greater than 1. A = {  2,3,4 } now B which is a subset. of A can be any one of these: B = { 2,3} or B = {2} or B = { 3,4} etc. but not that B has no element other than that of A.

Even a null set is a sub-set of all the set may it be any set. A set of numbers can be either a set of real numbers or a set of integers or a set of fractions or a set of floating point number etc.  A set of numbers hence can be considered as a superset of all the other sets. A super set is which that contains all the sets elements of the given sub-sets. In the above example A can be called a superset of B and B can be called a S. S of A or just Subsets of Numbers.

The sum of subsets of a particular set will make up that set. It should be noted that null set belongs to every set.
To explain the Subsets of integers we can take up another example. The subsets can be A (sub-set of I) : { -1, -2 , 0 ,1, 2, 3} etc. All subsets are the part of a universal set which contains all the numbers. For a S. s of a integer we can have as many numbers as there are integers and then we can add a null set to it to get the original set.

The Set and Subset are the essentials for analyzing particular type of data and hence should be understood very clearly. The proper set and the improper set are yet another types of set, in a proper set we also have null element or entity. Similarly we can define s. s. for the same set.
R denotes the set of real numbers. Say ‘r’ is a s. s. of real numbers we write it as r = {0}

Percentage Increase

When we get a discount at a shop, we say that we got this much % off.  Now if the same shop offers 5 % more off, then the price of a product will be decreased by a certain amount. The increase and decrease in anything is usually calculated in terms of %. This is actually the measure of perc change which helps us to know the extent to which a thing has gained or lost its value over time.

For example if Sam works at shop with the pay of $ 10 per hour and if his pay gets increased to 4 15 per hour then we can Find Percentage Increase in his pay by making use of Formula for Percentage Increase which is difference of old value and new value divided by old value multiplied by hundred which can be written as (new value – old value) / old value X 100. Some more example of this would be change in temperature in two days, change in height or weight gain in children, share prices of a company or stock market or the prices of any product in a specific year compared to the last year.

How do you Calculate Percentage Increase- Finding Percentage Increase is done by following the series of steps given below: -

1. In the first step, we find out the difference between the two numbers.
2. In the second step, we take the difference and divide it by the original number.
3. In the third step, we multiply the number obtained in second step by 100.
4. In the last step, we put a % sign with the number or figure obtained in the third step.

Let us take an example to understand this concept more clearly. If the staff of a company is increased from 20 to 30 in one year then what is the Increase Percentage? To solve this, we follow the same steps given above. First we find the difference between two numbers which is 30 - 20 = 10. Then in the next step, we divide 10 by 20, which is the original number. That gives 10/20. Now in the next step, we multiply it by 100 which give 50. And in the last step, we put a 5 sign with 50 which makes the solution as 50 %.

Less than symbol

Less than symbol
A less than symbol looks like this “ <”  which is commonly used in mathematics. A less than symbol shows the relationship between in two values. The value that is on the left hand side is less than the value that is on the right hand is a less than symbol.

What is less than Symbol? In a way we can think about this is symbol with, two lines when they meet it becomes a point and that is where we put smaller value. But the Right hand side it is open wide and that side we put larger value. So for example if we are putting number 3 and number 5 like this, 3 less than(<) 5 Here we will put 3 at the left side and number 5 at right side, so we can say 3 is less than 5, this is less than sign example.

Symbols less than can be useful when we do not know the value of something, but we can compare to a value, we know that it is less than a certain value. So for instance I can never remember how old is my cousin sister is. But I know that she is younger to me. Let us say I am 20 years old, but I do know my cousin sister’s age is less than 20 years old. So we can write like this, age of my cousin < 20 years. Here we can say by looking this less than symbol, that age of my cousin sister is less than 20 years.

Another example in math symbols less than we shall understand it by, let us say that I have the expression 12 times 6 less than 8000,that is 12*6 < 8000 Maybe I cannot do that very quickly in my head but I am pretty confident that whatever I get 12 times 6 is going to be less than 8000. So there are times, in which we know rules of relationship between two numbers and which we can demonstrate it with the less than symbol.

The less than symbol does not tell us, how much less one value than the other is. It just puts them in that order. Which indicates one portion is smaller than the other. So let us use few more examples, where we can use less than symbols. Let us say, 7 and 56 can we use less than symbol here? Yes, very much as we know on the left side 7 and on the right side 56, so as per the symbol indicates <   56 is larger than 7. So we can use less than symbol here. Thus we can write 7 < 56.

Word Problems on Subtraction

Word problem is a very important concept of basic mathematics. A Word problem is nothing but a textual representation of a mathematical operation. Word problems are usually used to solve a problem easily. Word problems can be on all four operations of mathematics including addition, subtraction, multiplication and division. Let’s have a look at word problems on subtraction.
Word problem on subtraction is nothing but a text representation of subtraction. For example: Rohan bought 6 toys from Melissa & Doug brand. He gave 2 Melissa & Doug toys to Sam’s child and kept the others for his son. How many toys is he left with? This word problem is a text representation of mathematical problem (6 toys – 2 toys =?).

Solving word problems on subtraction:

Solving word problems on subtraction includes certain steps.  Firstly, both the numbers to be subtracted needs to be identified. Secondly, the word problem needs to be converted to a mathematical expression and finally, the number needs to be subtracted. For example: Mohan gifts three maternity wear from Mother Care India brand to his wife. His wife gives one of the Mother Care India maternity wear to her friend. How many maternity wear does Mohan’s wife now? Identifying the numbers, we get 3 maternity wear and 1 maternity wear. Converting the word problem to a mathematical expression and then subtracting, (3-1 = 2). Thus, the answer is 2 maternity wear.

Examples of Word Problems on Subtraction:

1. Philip has bought five fun toys from baby store India online collection. He gave two toys to Rohan’s son and kept one for his own son. How many toys from baby store India online does his son get?
Answer: 5 toys – 2 toys
(5-2) = 3 toys.
2. There are 18 Angry Bird toys in a basket. 7 Angry Bird toys were given to Mohan and 2 toys to Divya. How many Angry Bird toys were there in the basket after giving toys to Mohan and Divya?
Answer: 18 Angry Bird toys – 7 Angry Bird toys – 2 toys
(18-7-2) = 9 toys.
These are some basic examples on word problems on subtraction.

First, Second and Third Person in English

First person, second person and third person is one of the most important concepts in English learning. Grammatical person in English linguistics refers to a set of personal pronouns such as I, we, you, he, and she and so on. Let’s have a closer look at each of the grammatical persons – first, second and third, along with relevant examples in this post.

First Person
‘I’ is first person singular and ‘we’ is first person plural. First person refers to a narrator who speaks being a direct character. For example: I have tried shopping kids’ shoes online and I must tell you it was a nice experience and also the kids’ shoes online collection was huge. (Here, the speaker is speaking in first person.

Second Person
When a person is speaking as a second person, he or she is directly addressing the audience. The only three examples of second persons in English language are you, your and yours. For example: Did you know that online baby stores bring really good stuffs. You get kids’ dress from popular brands like Little Kangaroos India collection and kids’ toys from Little Tikes India collection. Also you will not believe the amount of discounts available for Little Kangaroos India brand and Little Tikes brand. (Here, the speaker is addressing the audience directly and is in second person.

Third Person
Third person as the term suggests is that where a speaker talks about some third person. Examples of third persons are he, she, it, him, her, it and more. Singular third person is he, she and it and plural third person are they, the, these, that and so on. For example: Mary is a school teacher. She got married in an early age and has a baby at 26 now. She buys almost every essential for her baby through online shopping. Online shopping is the latest trend of market and online shopping for kids has entered in the life of parents as savior. (Here, the speaker is talking about some third person to the audience.)
These are the basic learning on narrator, narration and narrative.

Conjunctions and its Types

Conjunction is one of the eight parts of speech in English grammar, the other seven being noun, pronoun, verb, adverb, adjective, preposition and interjection. Let’s have a look at conjunction and its types along with examples used in combining sentences, words and phrases in this post. Conjunction is a part of speech that combines two words, phrases or sentences together. For example:
Maria bought flora pencils for her daughter
Maria bough curved scissors for her daughter.
Maria bought flora pencils  and curved scissors for her daughter.  (Here, ‘and’ is the conjunction that connects the two sentences together.
There are two broad classifications of conjunction – Coordinating Conjunctions and Subordinating Conjunctions.

Coordinating Conjunctions: 
When a conjunction is used to combine two meaningful sentences of equal importance, it is called coordinating conjunctions. Coordinating conjunctions are also termed as coordinators. In English grammar, the coordinators to combine sentences are for, and, nor, either, neither, but, or, yet, so etc. For example:
• She will either buy Kittens shoes: or Disney shoes for her baby.
• Neither he drinks nor does he smoke.
• He is poor but humble.
• Online shopping is easy yet affordable.
• She brought apples and oranges from the market.

Subordinating Conjunctions:
When a conjunction combines two sentences where one of the sentences depends on the other to convey a complete meaning, it is called subordinating conjunctions. Subordinating conjunctions are also called subordinators. Subordinators combine and independent clause and a dependent clause to convey a complete meaning. Some of the most popular subordinators used in English grammar are: after, although, as, as far as, as long as, as soon as, because, since, whenever, whereas, while, since and more.  For example:
• As soon as she heard of online baby shopping, she rushed to buy baby food.
• Whenever he comes, it rains.
• Since I left the city, I have never been there again.
• While I was shopping online, I availed a discount coupon of branded stuff.
• He has not come today because he is ill.
These are some of the basics on conjunction and its types.

Understanding the laws of Boolean Logic

There have been various laws in the arithmetic number system. The study of these laws aids in the solving of various mathematical problems. The Boolean algebra laws are the laws concerning the logic 0 and 1. Only zero and one are used in the Boolean algebra. Sometimes true or false is also used to represent the same logic. Ultimately they represent nothing but on and off of supply of flow of current in an electric circuit.

The operations used in this algebra are similar to the laws in the algebra. There are certain basic differences and the notations might change. But the process is similar and simple. The Boolean laws can be conjunction, disjunction and negation. Conjunction is nothing but the process of multiplication that is present in the real numbers algebra. Dis junction is the process similar to addition that is done in the real number algebra. Negation is nothing but taking the negative of the given value. If the given value is x, then it is replaced by ‘-x’ in the process of negation.

This algebra was developed by Boole in the year 1840 and that is why it is known as Boolean algebra. It is used in digital electronics. It is very helpful in the analysis of various gates and circuits. It has certain laws and these have to be learnt to understand and solve the problems. The Boolean laws are to be learnt for this and they are quite simple to learn. There can be different variables used in this algebra but these variables can have only two values zero and one. A large expression can be formed with the help of the variables.

These are to be solved with the help of laws of Boolean algebra and understood. The variables like A, B, X, Y can be used to represent the variables in this algebra and then the expressions formed and the logical operations carried out. Any variable added to ‘1’ gives one. This is one of the laws. Any variable added to zero gives the same variable. Any variable multiplied with ‘1’ gives the same variable. The same variable if multiplied with ‘0’ gives ‘0’. In electronics it represents an open circuit. Two similar variables on addition give the same variable. Multiplication of two similar variables gives the same variable. Commutative property of addition also holds good. These are some of the laws. The variables can take values 0 and 1 only.