Collection of Multiple choice questions and Answers (MCQs) focuses on “Set Theory” along with their solution and justification.
Let and
, then which of the following statements is correct?
(A) in
(B) with respect to
(C) with respect to
(D) with respect to
Answer: (C)
We have, in
The set of elements in
which are not in
in
is false, because
is not an element of
in
in
is false, because
is not an element of
in
in
is correct, because the only element of
namely
also belongs to
in
.
in
is false, because
is not a set.
If ,
,
and
then
is
(A) 9
(B) 8
(C) 6
(D) None of these
Answer: (A)
Explanation:
We have,
Now,
Two finite sets have and
elements, then total number of subsets of the first set is 56 more that the total number of subsets of the second. The values of
and
are,
(A) 7, 6
(B) 6, 3
(D) 5, 1
(D) 8, 7
Solution: (B)
Since the two finite sets have and
elements, so number of subsets of these sets will be
and
respectively. According to the question
putting ,
, we get
or
If A has 3 elements and B has 6 elements, then the minimum number of elements in the set is
(A) 6
(B) 3
(C)
(D) None of these
Answer: (A)
Clearly the number of elements in will be minimum when
. Hence the minimum number of elements in
is the same as the number of elements in B, that is, 6.
Solution: (A)
Clearly the number of elements in will be minimum when
. Hence the minimum number of elements in
is the same as the number of elements in