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Algebra as Patterns

Write the fol...

Question

Write the following sets in roster (Tabular) form:

(i) $A_{1} = {x : 2 x + 3 = 11}$

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Solution

Step : Express the given set in roster (Tabular) form:

We know that in roster or tabular method, the elements of the set are written inside a pair of curly braces and are separated by commas.

Given:

$A_{1} = {x : 2 x + 3 = 11}$

$\Rightarrow 2 x + 3 = 11$

$\Rightarrow 2 x = 11 - 3$

$\Rightarrow 2 x = 8$

$\Rightarrow x = \frac{8}{2}$

$\Rightarrow x = 4$

Hence, the set $A_{1} = {x : 2 x + 3 = 11}$ in roster (Tabular) form is $A_{1} = {4}$ .

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(ii) $B_{2} = {11, 13, 17, 19.........}$

(iii) $B_{3} = {\frac{1}{3}, \frac{3}{5}, \frac{5}{7}, \frac{7}{9}, \frac{9}{11} . . . . . . . . .}$

(iv) $B_{4} = {8, 27, 64, 125, 216.........}$

(v) $B_{5} = {- 5, - 4, - 3, - 2, - 1.........}$

(vi) $B_{6} = {. . . . . . . . . . . - 6, - 3, 0, 3, 6.........}$

A = {x : x is an integer and - 3 < x < 7}

B = {x : x is a natural number less than 6}

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Write the following cubes in expanded form:

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A_{3} = {x : x ϵ z, - 3 \leq x < 4}