Aspire Faculty ID #17776 · Topic: JAMIA MILLIA ISLAMIA MCA 2025 · Just now
JAMIA MILLIA ISLAMIA MCA 2025

Let R be a relation on the set of ordered pairs of positive integers such that ((p, q), (r, s)) ∈ R if and only if p − s = q − r. Which one of the following is true about R?

Solution

Let R be a relation on ordered pairs of positive integers such that ((p,q),(r,s)) R iff p-s=q-r Check reflexive: For reflexive, take (p,q)=(r,s) Then condition becomes p-q=q-p 2p=2q p=q This is not true for every ordered pair, so R is not reflexive. Check symmetric: Given p-s=q-r Rearrange: p+r=q+s Now for symmetry we need r-q=s-p This also gives r+p=s+q, same condition. So R is symmetric.
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