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Laws of Algebra of Set
Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A (ii) A ∩ A = {x : x…
Function as a Machine
Function as a machine A function can also be regarded as a machine that gives unique output in set B corresponding to each input from the set A just as the function ‘machine’ shown in Fig. 2(b). Which generate an output y = 2×3 + 5 for each input x. Fig. 2(b) Usually real…
Range of Relation
Range of relation Let R be a relation from a set A to a set B. Then the of all second components or coordinates of the ordered pairs belonging to R is called the range of R. Thus, Range of R = { b : (a, b) ∈ R} Clearly, range of R ⊆ B…
Venn Diagrams | Set
Venn diagrams The diagram drawn to represent sets are called Venn-diagram. In Venn-diagram the universal set U is represented by points within the rectangle and its subsets are represented points in closed curves (usually circles) within the rectangle. If a set A is a subset of a set B, then the circles representing A is…
Ordered Pairs and Equality of an Ordered Pairs
Ordered pairs An ordered pairs consists of two objects or elements in a given fixed order. For example, if A and B are any two sets, then by an ordered pair of elements we mean a pair (a, b) in that order, where a ∈ A, b ∈…
Union of sets
Union of sets Let A and B be two sets. The union of A and B is the set of all those elements which belong either to A or to B or to both A and B. We denote A union B by notation “A ∪ B” Thus A∪B = { x : x ∈…
Laws of Algebra of Set
Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A (ii) A ∩ A = {x : x…
Function as a Machine
Function as a machine A function can also be regarded as a machine that gives unique output in set B corresponding to each input from the set A just as the function ‘machine’ shown in Fig. 2(b). Which generate an output y = 2×3 + 5 for each input x. Fig. 2(b) Usually real…
Range of Relation
Range of relation Let R be a relation from a set A to a set B. Then the of all second components or coordinates of the ordered pairs belonging to R is called the range of R. Thus, Range of R = { b : (a, b) ∈ R} Clearly, range of R ⊆ B…
Venn Diagrams | Set
Venn diagrams The diagram drawn to represent sets are called Venn-diagram. In Venn-diagram the universal set U is represented by points within the rectangle and its subsets are represented points in closed curves (usually circles) within the rectangle. If a set A is a subset of a set B, then the circles representing A is…
Ordered Pairs and Equality of an Ordered Pairs
Ordered pairs An ordered pairs consists of two objects or elements in a given fixed order. For example, if A and B are any two sets, then by an ordered pair of elements we mean a pair (a, b) in that order, where a ∈ A, b ∈…
Union of sets
Union of sets Let A and B be two sets. The union of A and B is the set of all those elements which belong either to A or to B or to both A and B. We denote A union B by notation “A ∪ B” Thus A∪B = { x : x ∈…
Laws of Algebra of Set
Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A (ii) A ∩ A = {x : x…
Function as a Machine
Function as a machine A function can also be regarded as a machine that gives unique output in set B corresponding to each input from the set A just as the function ‘machine’ shown in Fig. 2(b). Which generate an output y = 2×3 + 5 for each input x. Fig. 2(b) Usually real…