Addition And Multiplication Laws Of Real Number

Addition and multiplication laws of real number

(1) Addition Laws of real number

(i) Closure Law of addition

∀ a, b ∈ R (for all a, b is a part of real number)

such that

∀ a + b ∈ R (for all a + b is a part of real number)

(ii) Associative Law of Addition

∀ a, b, c ∈ R (for all a, b, c is a part of real number)

Such that

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

(iii) Additive identity

∀ a ∈ R And ∃ (there exist) 0 ∈ R

Such that

a +0 = 0 + a = a

(iv) Additive Inverse

∀ a ∈ R And ∃ (there exist) – a ∈ R

Such That

a + (-a) = 0 = (- a) + a

(v) commutative Law of Addition

∀ a, b ∈ R (for all a, b is a part of real number)

Such that

a + b = b + a

Addition and multiplication laws of real number

(2) Multiplicative Law of Real number

(i) Closure Law multiplication

∀ a, b ∈ R (for all a, b “is a part” of real number)

a × b ∈ R

(ii) Associative Law multiplication

∀ a, b, c ∈ R (for all a, b, c is a “part” of real number)

Such that

a × (b × c) = (a × b) × c

(iii) Multiplicative Identity

∀ a ∈ R And ∃ (there exist) 1 ∈ R

Such that

a × 1 = 1 × a = a

1 is called the multiplicative identity of real number

(iv) multiplicative Inverse

∀ a (≠ 0) ∈ R And ∃ (there exist) a ‾¹ ∈ R

Such That

a × a ‾¹ = a ‾¹ × a = 1 (a ‾¹ is also written as 1 / a)

(v) Commutative law of multiplication

∀ a, b ∈ R (for all a, b is a part of real number)

Such that

a × b = b × a