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
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