LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SET BUILDER METHOD

**SET BUILDER METHOD – **

**In this method a set is defined by stating properties which
the statement of the set must satisfy. We use braces { } to write set in this
form. The brace on the left is followed by a lower-case italic letter that
represents any element of the given set. This letter is followed by a vertical
bar and the brace on the right. Symbolically, it is of the form {x ǀ
-}. Here we write the condition which ‘x’ satisfies, or more briefly, {x ǀ
P(x)}, P(x) is a proposition stating a condition for x. The x is a sort of place
holder, for all possible elements ‘x’ that have the given property. The
vertical line is a symbol for ‘such that’ and the symbolic form A = {x ǀ x is
even} reads “A is the set of numbers x such that ‘x’ is even. Sometimes a colon
(:) or a semicolon (;) is also used in place of the vertical bar.”**

** { x ǀ 7
< x < 15 and x ∈ N }**

** The set of all elements x such
that x has the given properties**

**Example.1) Write
the following sets in the set builder form.**

**(a)
The number 1, 3, 5,……….**

**Ans.) {x ǀ x is an odd number}**

**(b)
The solution of the equation x²+ 11x + 24 = 0**

**Ans.) {x : x²
+ 11x + 24 = 0}**

** 4 5 6 7 8 9**

**(c) F = { -------, -------, -------, -------, -------, ------ }**

** 7 8 9 10 11 12**

**We observe that in the given set, the
denominator of each fraction is 3 more than the numerator. Hence the set
builder form of the set is -**

** n**

** F = { x
ǀ x = --------, n ∈ N
and 4 ≤ x ≤ 9 }**

** n + 3**

**(d) {0, 1, 16, 84, 256, 625, 1296}**

**Ans.) We observe that the elements of the given set
are the cubes of the first seven whole numbers. In the set builder form C = {x
ǀ x = n⁴, n ∈ W and n ≤ 6}**

Your second block of text...