Define the following terms with example in the notebook. Also learn all the definition by heart.
Answers
1) Prime numbers
In math, prime numbers are whole numbers greater than 1, that have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself.
2) Composite numbers
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.
3) State two properties of HCF by division method
(i) The H.C.F. of two or more numbers cannot be greater than any one of them. For example, the H.C.F. of 16, 18 and 24 is 2 which is less than all the given numbers.
(ii) If one number is a factor of the other numbers, their H.C.F.
4) LCM
The Least Common Multiple ( LCM ) is also referred to as the Lowest Common Multiple ( LCM ) and Least Common Divisor ( LCD) . For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.
For example, LCM(2,3) = 6 and LCM(6,10) = 30.
5) Sets and their elements
Sets are usually symbolized by uppercase, italicized, boldface letters such as A, B, S, or Z. Each object or number in a set is called a member or element of the set. Examples include the set of all computers in the world, the set of all apples on a tree, and the set of all irrational numbers between 0 and 1.
6) Finite and infinite sets
Informally, a finite set is a set which one could in principle count and finish counting. For example, is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite.
7) Equal and equivalent sets
Equal sets have the exact same elements in them, even though they could be out of order. Equivalent sets have different elements but have the same amount of elements. ... A set's cardinality is the number of elements in the set. Therefore, if two sets have the same cardinality, they are equivalent!
8) Proper subset
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion.
9) Face value
Face value is a financial term used to describe the nominal or dollar value of a security, as stated by its issuer. For stocks, the face value is the original cost of the stock, as listed on the certificate. For bonds, it is the amount paid to the holder at maturity, typically in $1,000 denominations.
10) State any two properties of addition
There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties. Additive Identity Property: The sum of any number and zero is the original number.
For example 5 + 0 = 5.
11) State any two properties of substraction
Closure property: For any two whole numbers, a and b, if a > b then a – b is a whole number and if a < b then a – b is never a whole number.
Commutative property: For any two whole numbers a and b, a – b ≠ b – a . Hence subtraction of whole number is not commutative.
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