MTH100 Subjective Notes

Mid term Practice exercises and important Questions

1) Write the following expression in the form of a

ib

i i i i

( 1) ( 1) i i i i i i i i i i i i i i

i i i i i i i i i i i i

2) Write in set builder notation

A= Set of first 100 odd numbers

A= Set of Natural numbers starting from 2 to 40. A= Set of all even numbers greater than 50.

A = {x| x is set of first 100 odd numbers}

A = {x|2≤x≤40 and x is set of natural numbers}

A = {x|x>50 and x is set of even numbers}

3) List the elements of the set (roster method)

10} A x x E x Î Ù £ 9, A x x x is even 10} A x x N x Î Ù £ A = {x | x is a person taller than 15 feet} B = {x | x2 = 16, x is odd} Set of first five multiples of 3.

A = {0,2,4,6,8,10}

A = ∅

A = {2,3,4,5,6,7,8,9,10} A= ∅ A=∅

A = {3,6,9,12,15}

Q4. Let A be the set of all even numbers. Let B be the set of all Number less than 100. Is A a subset of B? or Is B a subset of A?

A⊄B

B⊄A

List all elements in these sets and verify the result.

5) Let A={2,4,6,8,10,12,14,16,18,20} B={1,3,5,7,9,11,13,15,17,19,21}

Find A ∩ B and A Ụ B.

A ∩ B = { ∅ } and A Ụ B = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21}

Q6. Let A be all multiples of 6 and B be all multiples of 3. Is A a subset of B? And is B a subset of A?

A= {6,12,18,24,30,36,.......} B={3,6,9,12,15,18,21,24,......} A is subset of B but B is not subset of A.

7) The complex numbers Z is given by

i Z i Find modulus of Z .

Answer: B intersection C is shown in red. If we take the union of this red portion with the A then it will be like

So the total colored region (red + orange) is the required region.

Solve all other on the same lines.

Q11. What is the cardinality of these sets?

A = Set of even integers ∞

B = Set of prime numbers less than 30 ∞

C={11,12,13,14,15,16,17,18}

12. State the Associative Law for union and intersection.

A∪ (B∪C) = (A∪B) ∪C

A∩ (B∩C) = (A∩B) ∩C

13)

then find

z z

Solution:

z i