Question

say what is mean closure ,commutative ,assosiative ,distributive property . give three examples of each

Answer 1

closure property= The Closure Property states that when you perform an operation (such as addition, multiplication, etc.) on any two numbers in a set, the result of the computation is another number in the same set .

example: 1+2=3

              8*2=16

               2/2=1

commutative property: In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it

example: 1+2=2+1

                5+1=1+5

                4*5=5*4

note: holds true only for addition and multiplication.

associative property:In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs

example: 7+(3+6)= (7+3)+6

                2 + (3 + 4) = (2 + 3) + 4

                 2(3×4) = (2×3)4

note: does not hold true for division and subtraction.

distributive property:In mathematics, the distributive property of binary operations generalizes the distributive law from Boolean algebra and elementary algebra. In propositional logic, distribution refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and dis junctions within logical proofs.

example: 3x6 = (3x2)+(3x4)

              a(b + c) = ab + ac.

              7*(2+3)=7*2+7*3

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Answer 2

closure commutative assositative