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For real number x and y, we writeis an irrational
number. Then the relation R is:
a)Reflexive
b)Symmetric
c)Transitive
d)Equivalence
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For real number x and y, we writeis an irrationalnumber. Then the rela...
xRy => x - y + √2 is an irrational number.
Let R is a binary relation on real numbers x and y.
Now, R is transitive iff for all (x, y) ∈ R and (y, z) ∈ R implies (x, z) ∈ R
Given, xRy => x - y + √2 is irrational ............1
and yRz => y - z + √2 is irrational ............2
Add equation 1 and 2, we get
(x - y + √2) + (y - z + √2) is irrational
= x - z + √2 is irrational
= xRz is irrational
So, the relation R is transitive.
Most Upvoted Answer
For real number x and y, we writeis an irrationalnumber. Then the rela...
It must be reflexive because if x=y it becomes root 2 which is an irrational number. it is not symmetric because x-y+root2 not=y-x+root2
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Community Answer
For real number x and y, we writeis an irrationalnumber. Then the rela...
Reflexive Relation:
A relation R on a set A is said to be reflexive if every element of A is related to itself. In other words, for every element a ∈ A, (a, a) ∈ R.
Explanation:
In this case, the relation R is defined as "x - y is an irrational number". Let's check if the relation R is reflexive.
Step 1: Choose an arbitrary element a from the given set of real numbers.
Let's consider a = 5. Since 5 is a real number, it satisfies the condition for x and y in the relation R.
Step 2: Check if (a, a) ∈ R.
To satisfy the relation R, we need to check if 5 - 5 is an irrational number.
5 - 5 = 0, which is a rational number, not an irrational number.
Step 3: Conclusion
Since (a, a) = (5, 5) does not satisfy the condition for the relation R, the relation R is not reflexive.
Correct Answer:
The correct answer is not option 'A' (Reflexive). The relation R is not reflexive.
A relation R on a set A is said to be reflexive if every element of A is related to itself. In other words, for every element a ∈ A, (a, a) ∈ R.
Explanation:
In this case, the relation R is defined as "x - y is an irrational number". Let's check if the relation R is reflexive.
Step 1: Choose an arbitrary element a from the given set of real numbers.
Let's consider a = 5. Since 5 is a real number, it satisfies the condition for x and y in the relation R.
Step 2: Check if (a, a) ∈ R.
To satisfy the relation R, we need to check if 5 - 5 is an irrational number.
5 - 5 = 0, which is a rational number, not an irrational number.
Step 3: Conclusion
Since (a, a) = (5, 5) does not satisfy the condition for the relation R, the relation R is not reflexive.
Correct Answer:
The correct answer is not option 'A' (Reflexive). The relation R is not reflexive.
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For real number x and y, we writeis an irrationalnumber. Then the relation R is:a)Reflexiveb)Symmetricc)Transitived)EquivalenceCorrect answer is option 'A'. Can you explain this answer?
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