Let A = N × N be the Certesian product of N and N. Let
S = {((m, n), (p, q)) ∈ A × A : m + q = n + p}
Consider the following statements:
I.If ((m,n), (p , q)) ∈ S, and ((p,q), (r, s)) ∈ S then ((r,s), (m,n)) ∈ S
II.There exists at least one element ((m,n), (p, q)) ∈ S such that ((p , q), (m, n)) ∉ S
Which of the statements given above is / are correct ?
Text Solution
Verified by ExpertsA
((m,n) ,(p,q)) ∈ S
⇒ m + q = n + p
((p,q) , (r,s)) ∈ S ⇒ p + s = r + q
⇒ ((r,s) , (m,n)) ∈ s
as r + n = m + s
Now if we add above equation
((m,n) , (p,q)) ∈ s ⇒ m + q = n + p
⇒ (n+p) = m + q & hence ((P,q) , (m,n))
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