Maths-
General
Easy
Question
Let
be a relation on a set
such that
then
is
- Reflexive
- Symmetric
- Transitive
- None of these
The correct answer is: Symmetric
Let
Then,
[By def. of
]
![left square bracket because R equals R to the power of negative 1 end exponent right square bracket](data:image/png;base64,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)
So,
is symmetric
Related Questions to study
Maths-
Given
, where
is the universal set,
and
are subsets of
, then
equals to
Given
, where
is the universal set,
and
are subsets of
, then
equals to
Maths-General
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In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is
In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is
Maths-General
Maths-
Two finite sets have
and
elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then, the value of
and
are
Two finite sets have
and
elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then, the value of
and
are
Maths-General
Maths-
If
is a relation from a set
to a set
and
is a relation from
to a set
then the relation ![S o R](data:image/png;base64,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)
If
is a relation from a set
to a set
and
is a relation from
to a set
then the relation ![S o R](data:image/png;base64,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)
Maths-General
Maths-
If
is a non-empty set, then which of the following is false?
There is at least one reflexive relation on ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
There is at least one symmetric relation on ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
If
is a non-empty set, then which of the following is false?
There is at least one reflexive relation on ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
There is at least one symmetric relation on ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
Maths-General
Maths-
If a set
contains
elements, then which of the following cannot be the number of reflexive relations on the set ![A ?](data:image/png;base64,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)
If a set
contains
elements, then which of the following cannot be the number of reflexive relations on the set ![A ?](data:image/png;base64,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)
Maths-General
Maths-
If relation
is defined as :
if
is the father of
Then,
is
If relation
is defined as :
if
is the father of
Then,
is
Maths-General
Maths-
If
then how many subsets of
contain the elements
and ![5 ?](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAANCAYAAABPeYUaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYICA/3gwDPgB8WEg/gHEn4B4NhCLI8mjKMYFNgGxJRAzQfkeUENJMgQb+EGpISBXraHEEFsgXgzEPOiG/IIG2DYgLkJXgAQMgHghUthgABYgNgbiWiC+AcQaWNSAAlOQWCe7AfFBLOJ/KAp9coAOEN8lRcM6pITEBE1IIAOCsKjFGZOhQHwL6t93QLwKiE1xqP3PQAsAAE3WJzrHL45aAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj41PC9tbj48bW8+PzwvbW8+PC9tYXRoPkFIPoQAAAAASUVORK5CYII=)
If
then how many subsets of
contain the elements
and ![5 ?](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAANCAYAAABPeYUaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYICA/3gwDPgB8WEg/gHEn4B4NhCLI8mjKMYFNgGxJRAzQfkeUENJMgQb+EGpISBXraHEEFsgXgzEPOiG/IIG2DYgLkJXgAQMgHghUthgABYgNgbiWiC+AcQaWNSAAlOQWCe7AfFBLOJ/KAp9coAOEN8lRcM6pITEBE1IIAOCsKjFGZOhQHwL6t93QLwKiE1xqP3PQAsAAE3WJzrHL45aAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj41PC9tbj48bW8+PzwvbW8+PC9tYXRoPkFIPoQAAAAASUVORK5CYII=)
Maths-General
Maths-
If
and
then the minimum possible value of
is
If
and
then the minimum possible value of
is
Maths-General
Maths-
Let
be a relation on the set
of natural numbers defined by
is a factor of
Then,
is
Let
be a relation on the set
of natural numbers defined by
is a factor of
Then,
is
Maths-General
Maths-
If
then the maximum number of elements in any relation on
is
If
then the maximum number of elements in any relation on
is
Maths-General
Maths-
If
and
then
is equal to
If
and
then
is equal to
Maths-General
Maths-
Let
be the set of all engineering colleges in a state of Indian Republic and
be a relation on
defined as two colleges are related iff they are affiliated to the same university, then
is
Let
be the set of all engineering colleges in a state of Indian Republic and
be a relation on
defined as two colleges are related iff they are affiliated to the same university, then
is
Maths-General
Maths-
Let
and
be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then,
is equal to
Let
and
be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then,
is equal to
Maths-General
Maths-
Let
. The total number of unordered pairs of disjoint subsets of
is equal to
Let
. The total number of unordered pairs of disjoint subsets of
is equal to
Maths-General