The relation R on the set N × N defined by (a, b) R(c, d) ⇔ a + d = b + c ∀ (a, b), (c, d), ∈ N × N is ,where N is set of natural number :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Equivalence
(1) Reflexive
for every $(a, b)∈N×N,(a+b)=(b+a)$
(2) Symmetric
for every $(a,b)R(c,d)$, $(a+b)=(c+d)$
$⇒(c+d)=(b+a)⇒(c,d)R(a,b)$
(3) Transitive
for every $(a,b)R(c,d),(c,d)R(e,f)$
$a+b=d+c,c+d=f+e$
$⇒a+b=f+e,⇒(a,b)R(e,f)$
⇒ Equivalence relation