Mathematics Exam > Mathematics Questions > Let P be the set of all p lanes in R 3. The r...
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Let P be the set of all p lanes in R 3. The relation being normal in P is
- a)symmetric and transitive
- b)symmetric and reflexive
- c)symmetric but not transitive
- d)transitive but not reflexive
Correct answer is option 'C'. Can you explain this answer?
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Let P be the set of all p lanes in R 3. The relation being normal in P...
Let P be the set of all planes in R3, The relation being normal in P is symmetric but not transitive.
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Let P be the set of all p lanes in R 3. The relation being normal in P...
Explanation:
In order to determine the properties of the given relation, let's first define the relation of being normal in the set of all planes in R^3.
Definition: A relation R on a set P is said to be normal if for any two distinct planes A and B in P, A is normal to B implies that B is normal to A.
Now, let's analyze the properties of the given relation:
Symmetric:
A relation R is said to be symmetric if for any two elements a and b in the set P, if a is related to b, then b is related to a. In this case, if plane A is normal to plane B, then plane B is also normal to plane A. Hence, the relation is symmetric.
Reflexive:
A relation R is said to be reflexive if for every element a in the set P, a is related to itself. In this case, a plane cannot be normal to itself. Hence, the relation is not reflexive.
Transitive:
A relation R is said to be transitive if for any three elements a, b, and c in the set P, if a is related to b and b is related to c, then a is related to c. In this case, if plane A is normal to plane B and plane B is normal to plane C, it does not necessarily imply that plane A is normal to plane C. Hence, the relation is not transitive.
Therefore, the relation of being normal in the set of all planes in R^3 is symmetric but not transitive. Hence, the correct answer is option C.
In order to determine the properties of the given relation, let's first define the relation of being normal in the set of all planes in R^3.
Definition: A relation R on a set P is said to be normal if for any two distinct planes A and B in P, A is normal to B implies that B is normal to A.
Now, let's analyze the properties of the given relation:
Symmetric:
A relation R is said to be symmetric if for any two elements a and b in the set P, if a is related to b, then b is related to a. In this case, if plane A is normal to plane B, then plane B is also normal to plane A. Hence, the relation is symmetric.
Reflexive:
A relation R is said to be reflexive if for every element a in the set P, a is related to itself. In this case, a plane cannot be normal to itself. Hence, the relation is not reflexive.
Transitive:
A relation R is said to be transitive if for any three elements a, b, and c in the set P, if a is related to b and b is related to c, then a is related to c. In this case, if plane A is normal to plane B and plane B is normal to plane C, it does not necessarily imply that plane A is normal to plane C. Hence, the relation is not transitive.
Therefore, the relation of being normal in the set of all planes in R^3 is symmetric but not transitive. Hence, the correct answer is option C.
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Community Answer
Let P be the set of all p lanes in R 3. The relation being normal in P...
A group G, {0},+) under addition operation satisfies which of the following properties?
The group G satisfies the properties of closure, associativity, inverse, and identity since there is only one element (0) in the set, making closure and identity trivial, and associativity and inverses are always satisfied for any group.
The group G satisfies the properties of closure, associativity, inverse, and identity since there is only one element (0) in the set, making closure and identity trivial, and associativity and inverses are always satisfied for any group.
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Let P be the set of all p lanes in R 3. The relation being normal in P isa)symmetric and transitiveb)symmetric and reflexivec)symmetric but not transitived)transitive but not reflexiveCorrect answer is option 'C'. Can you explain this answer?
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