Given: $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $R \subseteq A^2$, where $aRb \leftrightarrow b− a = 1$, give $R$ explicitly: $$R = ?$$
How would I got about solving this? I was thinking $R = \{[2,1],[3,2],[4,3],[5,4],[6,4],[7,6]\}$ since these are combinations result into 1.
What am I missing?
You're almost right, but you've got your tuples backwards. "$aRb$" means "$b-a=1$," so e.g. $1R2$, not $2R1$ as you've written, etc. (Note that order matters in relations, in general.)