Question 1: i) If (ii) if .

Answer:

By definition of equality of ordered pairs, we have

By definition of equality of ordered pairs, we have

Question 2: If the ordered pairs .

Answer:

The ordered pairs

Thus we have

Thus we get

Question 3: If , write the set of all ordered pairs .

Answer:

Since , we know that the possible ordered pairs are

Question 4: If , then form the set of all ordered pairs such that a divides .

Answer:

. Here

is less than all of them

is less than

is less than

Therefore set of all ordered pairs Hence

Question 5: If .

Answer:

Question 6: Let . Find and show it graphically.

Answer:

Question 7: If , and ?

Answer:

Question 8: If are two sets haying elements in common. It .

Answer:

Therefore

are two sets having elements in common

Let

Question 9: Let be two sets. Show that the sets have an element in common iff the sets have an element in common.

Answer:

Case 1: Let

Therefore they have no common elements.

Case 2: Let

Hence

Therefore will have common elements if and only if sets A and set B have elements in common.

Question 10: Let be two sets such that . If are in find where , and are distinct elements.

Answer:

Since are elements of , therefore

It is given that

Similarly,

Question 11: Let . Write explicitly.

Answer:

We know:

Question 12: If , find .

Answer:

Question 13: State whether each of the following statements are true or false. If the statement is false, re-write the given statement correctly:

(i) If , then

(ii) If are non-empty sets, then is a non-empty set of ordered pairs .

(iii) If , then

Answer:

i) False

If , then

ii) False

If are non-empty sets then is a non-empty set of ordered pairs .

iii) True

Question 14: If , form the set .

Answer:

Question 15: If , represent following sets graphically:

Answer: