Union of sets
If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..
Operations on Sets
Union of sets - If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..
Algebraic Properties of set operations
Idempotent laws - If A is any set,th..
Idempotent laws - If A is any set,th..Binary Operations
Binary Operations - Binary Operations are as given below, Commutative Law Associative Law Let S be any non-empty set. An operation * is called a binary operation on S if " a, b Î S a * b Î SLet S be any non-empty set. An h..
Binary Operations
binary operation: Let S be any non-empty set. An operation * is called a binary operation on S if " a, b S a * b S Commutative law: Let * be a binary operation on the set S. * is said to be associative in S if " a..
Logical 'OR' operation
Let us refer to a circuit consisting of two switches p and q connected in parallel with a lamp and battery as shown in figure. In this case, the lamp will glow if and only if at least one of the switches is closed. In binary language we say the switch will glow if at least one of the values of p..
Let us refer to a circuit consisting of two switches p and q connected in parallel with a lamp and battery as shown in figure. In this case, the lamp will glow if and only if at least one of the switches is closed. In binary language we say the switch will glow if at least one of the values of p..State whether the expression {x : x< 3} or {x : x> 10} represent..
State whether the expression { x : x < 3} or { x : x > 10} represents an intersection or union of sets. => disjunction or union or intersection or conjunction..
Boolean Algebra Introduction
Introduction - We are already familiar with set theory and mathematical logic from earlier classes. It has already been seen that there is a similarity between the laws stated in set theory and the mathematical logic. The operations 'union', 'intersection' an..
Boolean Algebra as an Algebraic Structure
Boolean Algebra is an algebraic structure defined by a set of elements B, together with two operations, + and . satisfying the following axioms (Hunington postulates..
Summary
A Boolean algebra is a set B with two distinct elements, along with the binary operations '+' and '.' and a unary operation (') which satisfy closure property, commutative property, existence of unit element, distributive property for both the binary operati..
Result
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