Basic Maths 23 May

BASIC MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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(A+B+C)^2 =? • A^2+B^2+C^2+2(AB+AC+BC)

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WHAT WILL YOU GET IF YOU DIVIDE (223^333123^333) BY 100. • YOU WILL GET ZERO • X^N-Y^N DIVIDED BY (X-Y) WILL GIVE ZERO AS REMAINER.

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WHAT IS A UNIVERSAL SET? • WHEN WE COMBILE ALL SETS, WE GET UNIVERSAL SET. • FOR EXAMPLE, • IF WE PREPARE SET OF NATURAL NUMBERS FROM 1 TO 100, OUR UNIVERSAL SET IS NATURAL NUMBERS’ SET.

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WHAT IS U IN SET THEORY? • U is union. When we combine two sets, it is called union of sets. • For example: • X = {1,2,3,4}, Y = {4,5,6,} • XUY = {1,2,3,4,5,6}

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What is in set theory? •

it is symbol of intersection

• For example: • X = {1,2,3,4}, Y = {4,5,6,} • X intersection Y = {,4,}

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How many subsets can you make from a set {1,2,3,4,} • You can make 2^n subsets – so 2^4 =16 • However one of the subsets is empty set. • Proper subsets are = 15.

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What is cardinal number of a set? • Distinct number of elements in a set is called cardinal number of a set. • For example: • X = {1,2,3,4}, cardinal number is 4.

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What is finite and infinite set? • When numbers are specified, it is called finite set. • When numbers are not limited, it is called infinite, for example, a set containing all the integer numbers less than 2 is called infinite set

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What is difference of set? • X = {1,2,3,4}, Y = {4,5,6,} • Now here difference X-Y is {1,2,3,} = what X has but y does not hav.e • Y- X = {5,6} - what Y has, but X doesn’t have. • Symmetric difference is sum total of Y-X and X-Y = {1,2,3,5,6,} www.afterschoool.tk

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What are cumulative and associative laws? • AUB = BUA • This is cumulative law. • In associative law – we have relation within relation: • AU(BUC) =(AUB)UC

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WHAT IS ADDITIVE IDENTITY OF 235? • Additive identity of any number is zero. • N+0= N • Therefore , additive identity of any number is 0.

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What is multiplicative identity of 234? • Multiplicative identity of any number is 1. • N*1 = N.

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What is trichonomy law regarding X and Y. • Tri means three - there are only three possibilities – • 1. either X is more than Y • 2. or X is equal to Y • 3. or X is less than y.

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What are the general symbols:

• N = natural number (natural numbers start from 1) • W = whole numbers (whole numbers start from 0 • I = integers (negative and positive numbers) • Q = rational numbers (where p/q holds) • R = real numbers • R>Q>I>W>N. www.afterschoool.tk

What is HCF? • HEIGHEST COMMON FACTOR is called HCF • For example: 12 and 15 have HCF: 3. ans.

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What is LCM? • Least Common Multiple is called LCM. • It is combined from different factors of two or more numbers. • What is LCM of 12 and 15: • 12=3*2*2, 15=3*5 • So LCM = 2*2*3*5 = 60 Ans.

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If LCM of two numbers is 5964 and HCF is 213, what are the numbers? • Step I ; divide 5964 by 213 – if it is divisible – there are two numbers otherwise none is possible. (you get 28) • Factors of 28 are 7*2*2 =so two groups are 7&4. • Combine the remaining numbers in different group – (213*4 and 213*7), – and you get two numbers as under: 852 and 1401. ans.

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If I INCREASE PRICE OF MY ITEM BY 40% AND THEN DECREASE BY 40%, WHAT IS THE RESULT?

• REMEMBER THE LAW : IN ALL SUCH CASES, (40*40)/100 = 16% NET DECREASE.

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If I INCREASE PRICE OF MY ITEM BY 20% AND THEN DECREASE BY 20%, WHAT IS THE RESULT?

• REMEMBER THE LAW : IN ALL SUCH CASES, (20*20)/100 = 4% NET DECREASE.

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