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)