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प्रश्न
The diagram represents two inequations A and B on real number lines:
- Write down A and B in set builder notation.
- Represent A ∪ B and A ∩ B' on two different number lines.
उत्तर
(i) Given:
A = {x ∈ R: -2 ≤ x < 5}
B = {x ∈ R: -4 ≤ x < 3}
(ii) A ∩ B = {x ∈ R: -2 ≤ x < 3}
It can be represented on number line as:
A ∩ B’ = A - B = {x ∈ R: 3 ≤ x < 5}
It can be represented on number line as:
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संबंधित प्रश्न
Use the real number line to find the range of values of x for which:
x > 3 and 0 < x < 6
Solve the following in equation write the solution set and represent it on the number line:
`-x/3 <= x/2 -1 1/3 < 1/6, x ∈ R`
Solve the following linear in-equation and graph the solution set on a real number line:
2x - 11≤ 7 - 3x, x ∈ N
Graph the solution set for each inequality:
5 ≤ x < 10
Given:
P = {x : 5 < 2x - 1 ≤ 11, x ∈ R}
Q = {x : -1 ≤ 3 + 4x < 23, x ∈ R}
Where R = (real number), I = (Integers) Reperesnr P and Q on number lines. Write down the elements of P ∩ Q.
Solve the following inequalities and represent the solution on a number line:
`(2x + 5)/(4) > (4 - 3x)/(6)`
Solve 2(x – 3)< 1, x ∈ {1, 2, 3, …. 10}
Solve `(3x)/(5) - (2x - 1)/(3)` > 1, x ∈ R and represent the solution set on the number line.
Solve the following inequation and represent the solution set on the number line : `4x - 19 < (3x)/(5) - 2 ≤ -(2)/(5) + x, x ∈ "R"`
The real number lines for two inequations A and B are as given below, A ∩ B is:
