Question 1: If the replacement set is the set of natural numbers (N), find the solution set of:

(i) (ii)

Answer:

Since, the replacement set = N (set of natural numbers) |
Since, the replacement set = N (set of natural numbers) |

Question 2: If the replacement set is the set of whole numbers (W), find the solution set of:

(i) (ii)

Answer:

Since, the replacement set = W (set of whole numbers) |
Since, the replacement set = W (set of whole numbers) |

Question 3: If the replacement set is the set of integers, (I or Z), between -6 and 8, find the solution set of: (i) (ii)

Answer:

Since, the replacement set = I (set of whole numbers between -6 and 8 ) |
Since, the replacement set = I (set of whole numbers between -6 and 8 ) |

Question 4: f the replacement set is the set of real numbers (R), find the solution set of :

(i) (ii)

Answer:

Since, the replacement set is the set of real numbers (R) |
Since, the replacement set is the set of real numbers (R) |

Answer:

Question 6: Solve the following equation:

(i) (ii)

Answer:

(i) When

Therefore Solution set

(ii) When

Therefore Solution set

Question 7: Given that , solve the following inequality and graph the solution on the number line: [ICSE Board 2006]

Answer:

Therefore Solution

Solution on the number line is :

Graph the values of on the real number line.

Answer:

The given inequation has two parts :

On simplifying, the given inequation reduces to and the required graph on number line is:

Question 9: List the solution set of given that Also represent the solution set obtained on a number line.

Answer:

The required solution set

And the required no. line is

Question 10: Solve and graph the solution set of and where

Answer:

And

Graph for

Graph for

Therefore graph of solution set of and

= Graph of points common to both and

Question 11: Solve and graph the solution set of or where

Answer:

Graph for

Graph for

Therefore graph of solution set of or

= Graph of points which belong to or or both

Question 12: Given:

Represent P and Q on two different number lines. Write down the elements of

Answer:

Question 13: Write down the range of values of for which both the inequations and are true.

Answer:

Both the given inequations are true in the range; where their graphs on the real number lines overlap.

The graphs for the given inequalities are drawn alongside.

It is clear from both the graphs that their common range is

Therefore required range is

Question 14: The diagram, given below, represents two inequations p and e on real number lines:

(i) Write down P and Q in set builder notation.

(ii) Represent each of the following sets on different number lines :

Answer:

(ii)

Question 15: Find three smallest consecutive whole numbers such that the difference between one-fourth of the largest and one-fifth of the smallest is at least 3

Answer:

Let the required whole numbers be

According to the given statement :

Since, the smallest value of that satisfies the inequation

Therefore Required smallest consecutive whole numbers are :