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In the set N x N, the relation R is defined by (a, b) R (c, d) ⇔  a+d = b+c. Then R is
a)symmetric and transitive but not reflexive
b)reflexive and transitive but not symmetric
c)Equivalence relation
d)Partial order relation
Correct answer is option 'C'. Can you explain this answer?
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In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = ...
The correct answer is c
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In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = ...
(a, b) R (c, d) <=> a + d = b + c
Reflexive:
(a, b) R (a, b) <=> a + b = b + a
This is true for all (a, b) € N x N
Hence, it is reflexive.
Symmetric:
Let (a, b) R (c, d) <=> a + d = b + c
a + d = b + c
c + b = d + a (same)
By the above equation,
(c, d) R (a, b)
Hence,
(c, d) R (a, b) <=> c + b = d + a
Hence, it is symmetric
Transitive:
Let (a, b) R (c, d) <=> a + d = b + c, --- eqn 1
(c, d) R (e, f) <=> c + f = d + e --- eqn 2
for all a, b, c, d, e, f € N
eqn 1 : a + d = b + c
⇒  a - b = c - d
eqn 2 : c + f = d + e
⇒ c - d = e - f
So, a-b = e-f
⇒ a + f = b + e
⇒ (a, b) R (e, f)
Hence, it is transitive.
This is an equivalence relation
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In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = ...
It is an equivalence relation . the correct answer is c
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In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = b+c. Then R isa)symmetric and transitive but not reflexiveb)reflexive and transitive but not symmetricc)Equivalence relationd)Partial order relationCorrect answer is option 'C'. Can you explain this answer?
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In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = b+c. Then R isa)symmetric and transitive but not reflexiveb)reflexive and transitive but not symmetricc)Equivalence relationd)Partial order relationCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = b+c. Then R isa)symmetric and transitive but not reflexiveb)reflexive and transitive but not symmetricc)Equivalence relationd)Partial order relationCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the set N x N, the relation R is defined by (a, b) R (c, d)⇔ a+d = b+c. Then R isa)symmetric and transitive but not reflexiveb)reflexive and transitive but not symmetricc)Equivalence relationd)Partial order relationCorrect answer is option 'C'. Can you explain this answer?.
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