Boolean Functions
Category : JEE Main & Advanced
Definition : Any expression like \[x\wedge x'\], \[a\wedge b'\], \[[a\wedge (b\vee c')]\vee (a'\wedge b'\,\wedge c)\] consisting of combinations by \[\vee \] and \[\wedge \] of finite number of elements of a Boolean Algebra B is called a boolean function.
Let \[B=\{a,b,c,....\}\] be a boolean algebra by a constant we mean any symbol as 0 and 1, which represents a specified element of B.
By a variable we mean a symbol which represents a arbitrary element of B
If in the expression \[{x}'\vee (y\wedge z)\] we replace \[\vee \] by + and \[\wedge \] by ., we get \[{x}'+y.z\]. Here \[{x}'\] and \[y\wedge z\] are called monomials and the whole expression \[{x}'\vee (y\wedge z)\] is called a polynomial.
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