number theory basic properties

: Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B. Cardinality of a Set A: The number of elements in a finite set A, is the cardinality of A and is denote..

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..

Addition and subtraction of two polynomials mean combining like terms. We can perform multiplication and division al..

(A T ) T = A (A + B) T = A T + B T , A and B being of the same order. (KA) T = KA T , k be any scalar (real or complex) (AB) T = B T A T ; A and B being conformable for the product A..

The Properties of Complex numbers are: Commutative Law for Addition, Commutative Law for multiplication, Additive Identity Exists, Multiplicative Identity Exist, Reciprocals (Multiplicative Inverses) Exist for nonzero complex numbers, Negatives (Additive Inverses..

If Z, Z 1 and Z 2 are complex numbers, th..

The Algebraic Properties of set operations are: Idempotent laws, Identity laws, Commutative laws, Associative laws, Distributive laws, De Morgan's Law..

Some Properties of A.P. - If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..

(1) A + B = B + A (Commutative property) (2) k(A + B) = kA + kB (Distributive property) (3) (A + B) + C = A + B + C (Distributive property) (4) (A + B) + C = A + (B + C) (Associative property) A + O = O + A = A where O is zero or null matrix. A = A + O (5) A ..

1. A.(adj A) = (adj A). A = |A| I 2. adj (AB) = (adj B) . (adj ..