Set – Theory

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Jun

Index

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Jun

Examples(2)

(6) Let A = { – 1, 0, 1, 2 } and B = { 0, 1, 4, 9, 16, 25 } & f : A $\large \rightarrow$ B

Let…

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01

Jun

Examples
(1) Write down the power set of A = { 10, 20, 30 }.

Soln. P (A) = { $\emptyset$ , {10}, {20}, {30}, {10, 20}, {10, 30}, {20, 30}, {10, 20, 30}…

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01

Jun

One-One & Many-One Functions
☼ One-One & Many-One Functions :   Let f : A $\large \rightarrow$ B. We say that f is one-one, if disti…

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01

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)

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01

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

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01

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 ) $\ne$

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01

Jun

Important Results From Venn Diagrams
☼ Important Results From Venn Diagrams ( As shown in Case – I ) : Let A and B be any two intersecting sets.

(i) n (A $\cup$ B) = n (A) + n (B) …

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01

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.

…

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01

Jun

Some More Important Results
☼ Some More Important Results :

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

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