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: