*Note: Refer to the following if you need clarifications. Reference on Numbers*

Question 1: State True or False:

i) : True

ii) : False

iii) : True

iv) : True

Question 2: State True or False: Given that , are real numbers and

i) If , then : True

ii) If , then : True

iii) If , then : False

iv) If , then : False

v) If ; then : True

vi) If , then : False

Question 3: If , find the solution set of the inequations:

i)

Answer

ii)

Answer:

Question 4: If the replacement set is a set of whole numbers, solve:

i)

Answer:

ii)

Answer:

iii)

Answer:

iv)

Answer:

Question 5: Solve the inequation: given that [1987]

Answer:

Question 6: If , find:

i) the smallest value of , when is a real number

ii) smallest value of when is an integer

Answer:

Therefore if is a real number the and if is an integer then

Question 7: If the replacement set is a set of real numbers, solve

i)

Answer:

ii)

Answer:

iii)

Answer:

iv)

Answer:

Question 8: Find the smallest value of for which , where .

Answer:

Therefore

Question 9: Find the largest value of for which and .

Answer:

Therefore

Question 10: Solve the inequation: and . [1999]

Answer:

Question 11: Given , find the solution set for

Answer:

Equation 1:

Equation 2:

Therefore

Question 12: , find the solution set for

Answer:

Equation 1:

Equation 2:

Therefore