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Q.33 only answer for transitivity part alone please

Q.33 only
answer for transitivity part alone please

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Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
let (a. b) and (b, c) belong to R.
so that a^2 + b^2 and b^2 + c^2 are both even
or a^2 + b^2 = 2m
and b^2 + c^2 = 2p for some m and p belonging to N
adding both eqns
a^2 + c^2 + 2b^2= 2(m+p)
or a^2 + c^2 = 2(m+p – b^2)= 2k, where k = m+p – b^2 also belongs to N since m, p, b all belong to N and a^2 + c^2 is bound to be positive.
hence, a^2 + c^2= 2k implies a^2 + c^2 is even.
whence (a, c) belong to R.
so R is transitive.
kindly approve :))

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