definitions

Parin Sir > definitions

Jun

Functions

☼ Functions : Let A and B be two non-empty sets. Then a rule f which associates to each x $\in$ A, a unique element f (x)

Posted in: Functions,

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Jun

Cartesian Product of Two Sets

☼ Cartesian Product of Two Sets : The Cartesian product A $\times$ B of two non-empty sets A and B is defined as : A

Posted in: Cartesian Product of Two Sets,

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Jun

Ordered Pair

☼ Ordered Pair : A pair of two elements a and b listed in a specific order, is called an ordered pair ( a, b ).

Note (i) ( 2, 3 ) $\ne$

Posted in: Ordered Pair,

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Jun

Venn Diagrams

☼ Venn Diagrams : We represent sets by closed bounded figures, known as Venn diagrams. The universal set is denoted by a rectangular region and each subset of it is shown by a closed bounded figure within this rectangle.

…

Posted in: Venn Diagrams,

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01

Jun

Some More Important Results
☼ Some More Important Results :

(i) A $\cup$ B = $\emptyset$

Posted in: Some More Important Results,

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01

Jun

Laws of operations
$\large \mapsto$ Commutative Laws :

(i) A $\cup$ B…

Posted in: Laws of operations,

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31

May

Complement of a Set
☼ Complement of a Set :   Let A be a subset of the universal set U, then the complement of A, denoted by Aٰ or A is defined by :

Aٰ = A = { x : x U, x A }.

Clearly, x A   x A.

e.g.

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31

May

Universal Set
☼ Universal Set :   In the discussion about sets, all sets are assumed to be the subsets of a definite set. This definite set is called the universal set. Universal set contains the sets under discussion as subsets. The symbol U i…

Posted in: Universal Set ,

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31

May

Symmetric Difference Of Sets
☼ Symmetric Difference Of Sets :   The symmetric difference of two sets A and B is defined by :

A $\triangle$ B   =   ( A

Posted in: Symmetric Difference Of Sets,

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