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(i) Roster Method
This method is also known as tabular method. In this method, a set is represented by listing all the elements of the set, the elements being separated by commas and are enclosed within flower brackets {..
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 factor in common viz., ..
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 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..Example 1:
01. 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 tru..
Suggested answer:
Let P(n) = n 2 - n + 41 is a prime number P(1) = (1) 2 - 1 + 41 = 41 is a prime number P(1) is true. P(2) = (2) 2 - 2 + 41 = 43 is a prime number P(2) is also true. P(41) = (41) 2 - 41 + 41 = (41) 2 is a prime number..
Let P(n) = n 2 - n + 41 is a prime number P(1) = (1) 2 - 1 + 41 = 41 is a prime number P(1) is true. P(2) = (2) 2 - 2 + 41 = 43 is a prime number P(2) is also true. P(41) = (41) 2 - 41 + 41 = (41) 2 is a prime number..Complex number
Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the type..
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 2
Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there are infinite numb..
Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there are infinite numb.. Result
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