Question
Let R be a relation over the set N×n and it is defined by (a, b) R (c, d) ⇒ a+ d = b + c. Then, R is
Answer: Option D
:
D
(a, b) R (a, b) because a + b = b + a. So, r is reflexive.
(a, b)R (c, d) ⇒ a+d = b+c ⇒ c+b = d+a
⇒ (c,d) R (a,b)
So, R is symmetric.
(a, b) R (c, d) and (c, d) R (e, f)
⇒ a + d = b + c, c + f = d + e
Adding, a + d + c + f = b + c + d +e
⇒ a + f = b + e
⇒ (a, b) R (e, f).
∴ R is transitive.
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:
D
(a, b) R (a, b) because a + b = b + a. So, r is reflexive.
(a, b)R (c, d) ⇒ a+d = b+c ⇒ c+b = d+a
⇒ (c,d) R (a,b)
So, R is symmetric.
(a, b) R (c, d) and (c, d) R (e, f)
⇒ a + d = b + c, c + f = d + e
Adding, a + d + c + f = b + c + d +e
⇒ a + f = b + e
⇒ (a, b) R (e, f).
∴ R is transitive.
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