Question 1: i) If find the values of and (ii) if , find the values of and .

Answer:

i)

By definition of equality of ordered pairs, we have

and

and

and

ii)

By definition of equality of ordered pairs, we have

and

and

Question 2: If the ordered pairs and belong to the set , find the values of and .

Answer:

The ordered pairs and belong to the set

Thus we have

and such that

Also and such that

Thus we get and

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

Answer:

Given and

Since , we know that the possible ordered pairs are

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

Answer:

Given and . Here

divides and is less than all of them

divides and is less than

divides and is less than and

Therefore set of all ordered pairs such that divides and Hence

Question 5: If , find and .

Answer:

Given

Question 6: Let and . Find and show it graphically.

Answer:

Given and

Question 7: If and , what are , and ?

Answer:

Given and

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

Answer:

Given and

Therefore

and are two sets having elements in common

Let

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

Answer:

Case 1: Let and

Therefore they have no common elements.

Case 2: Let and

Hence

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

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

Answer:

Since are elements of , therefore and

It is given that and

Similarly, and

Question 11: Let and divides . Write explicitly.

Answer:

Given

divides

We know: divides and

divides and

divides

divides

Question 12: If , find .

Answer:

Given

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 and , then

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

(iii) If , then

Answer:

i) False

If and , then

ii) False

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

iii) True

Question 14: If , form the set .

Answer:

Given

Question 15: If and , represent following sets graphically: (i) (ii) (iii) (iv)

Answer:

Given and

i)

ii)

iii)

iv)