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Numbers prime to each other
Such numbers have only 1 as common factor even though they may be composite numbers e.g., 21 and 32 are prime to each other. We generally write (21, 32) = 1, which means 21 and 32 are prime to each other i.e., they have only one..
Prime numbers and Composite numbers
A prime number is one that has only two factors namely 1 and itself. and a composite number has factors besides 1 and itsel..
Question 1
Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Kerala..
Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Kerala..Question 3
Question: What is a prime number? Answer: A number which has only two factors, namely 1 and then number itself is called a prime number..
Basic number theory question and answers
Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..
Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..Study the following examples
1. The numbers 2, 3, 5 and 8. 2. The solutions of the equation x 2 - 2x - 15 = 0. 3. The letters of the word "Chase". 4. People living in our locality. 5. The students Mary, Hillary, Catherine. 6. The workers who are absent from the factory. 7. The capital cities of Asia. 8. T..
Illustrative Examples
The following are the Illustrative Examples: If P(n) is the statement n 2 -n+41 is prime, prove that P(1), P(2) are true but P(41) is not true. Prove by P.M.I , n < 2 n for all n ..
Types of fractions
A Proper fraction has its numerator less than its denominator. An Improper fraction has its numerator greater than its denominator. A Mixed fraction consists of two parts, one is an integer and the other a proper fraction. Vulgar fraction is a fraction in which the denominat..
A Proper fraction has its numerator less than its denominator. An Improper fraction has its numerator greater than its denominator. A Mixed fraction consists of two parts, one is an integer and the other a proper fraction. Vulgar fraction is a fraction in which the denominat..Sets Summary
Summary - A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the properties which are satisfied by the elem..
Properties of Complex numbers
If Z, Z 1 and Z 2 are complex numbers, th..
If Z, Z 1 and Z 2 are complex numbers, th.. Result
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