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boolean algebra boolean algebra boolean algebra is logical calculation of the truth values it was developed by george boole in the year 1840 it is similar to the algebra of the real numbers but the binary operations like addition multiplication are replaced by logical operations operations of boolean algebra are 1 2 3 conjunction x^y-and or xy disjunction xy-or or x+y negation ¬x-not the boolean algebra turn out to match with set of operations 0 1 there are n number of arguments which will result in 22n operations the laws of the boolean algebra are called as theorems or semantics equations are called as axioms which result into logical outcomes know more about pie chart maker math.tutorvista.com page no 1/4

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p. 2

the approach axiomatic is complete because the result roves neither fewer or more laws than semantics it is algebra of two types of values these values are 0 and 1 or we can say them true or false and to get proper understanding of boolean algebra any two values can help to get the outcome each of the element of the boolean algebra ba is called as boolean function in computers multiplication is represented by and addition by or not with an over bar the operation of boolean which is closest to the numerical algebra is conjunction or multiplication 1 and 0=0 1 and 1 =1 in conjunction if two propositions are true the outcome will be true but if one is false the result will be false the various possibilities of the two propositions are represented by the truth table in disjunction which is same ad addition operation when both the values are true the result will true or we can say 1+1 =1 it will be false when both the proposition values are false means 0+0=0.it any of the proposition value is true the outcome will always be true .we can also says that conjunction is opposite of the disjunction negation is not similar to negative operator it is corresponding to the incrementation one property of negation is same to numerical negative operator which is if it is added twice it will return the same values this property is called as involution de morgans law is derived from this operation properties of boolean algebra b oolean algebra as set of elements x,y with the following properties learn more how to divide decimals math.tutorvista.com page no 2/4

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p. 3

1 it satisfy indempotent laws x ^x=x v x =x 2 commutative property xvy=yvx x^y y^x 3 associative property x y z x y z x vy v z x v y v z x x v y x vx y x4 absorption law 4 distributive operation x v y z x v y x v z x y v z x y v x ^z 4 duality property every statement which is valid must be having a dual which is found by complimenting the variables in the equation and interchanging the operations in the equation like and rules of boolean algebra suppose we have x y z as variables and these rules have justification for the various values 1 2 3 x+xy=x x+xy =x+y x+y x+z x+yz math.tutorvista.com page no 4/4

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p. 4

thank you for watching presentation

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