Addition Law Of Multiplication Of Real Number

Addition law of multiplication Always all number operation of addition lies is a part of the real number example we have three number a, b, c Addition operation on a, b, c is a part of real number. Addition law of multiplication of real number image.

Rule of addition law multiplication

∀ a, b, c ∈ R symbol ∀ means “always” ∈ means is a” part of ”

(i) a (b + c) = a b + b c (called distributivity of multiplication over addition)

(ii) (a + b)c = a c + b c

In addition to the above properties of real number posses the following properties

Properties of equality of real number (order properties)

Equality of numbers, denoted by = posses the following properties

(i) Reflexive property

∀ a ∈ R where a = a

(ii) symmetric property

∀ a, b ∈ R where a = b ⇒ b = a

(iii) Transitive property

∀ a, b, c ∈ R where a = b and b = c ⇒ a = c

(iv) Additive property

∀ a, b, c ∈ R where a = b ⇒ a + c = b + c

(v) Multiplicative property

∀ a, b, c ∈ R where a = b ⇒ a c = b c and c a = c b

(vi) Cancelation property w. r. t Addition

∀ a, b, c ∈ R where a + c = b + c ⇒ a = b

(vii) Cancelation property w. r. t Multiplication

∀ a, b, c ∈ R where a c = b c ⇒ a = b, c ≠ o