Let R be a relation on N×N defined by (a,b)R,(c,d)⇔a+d=b+c for all

1.	Let R be a relation on N×N defined by (a,b)R,(c,d)⇔a+d=b+c for all (a,b),(c,d)ϵN×N Show that : (i) (a, b) R (a, b) for all (a,b)ϵN×N (ii) (a,b)R(c,d)⇒(c,d)R(a,b) for all (a,b),(c,d)ϵN×N (iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ϵN×N.
Answer» Let R be a relation on $N \times N$ defined by $(a, b) R, (c, d) \Leftrightarrow a + d = b + c$ for all $(a, b), (c, d) ϵ N \times N$ Show that : (i) (a, b) R (a, b) for all $(a, b) ϵ N \times N$ (ii) $(a, b) R (c, d) \Rightarrow (c, d) R (a, b)$ for all $(a, b), (c, d) ϵ N \times N$ (iii) (a, b) R (c, d) and (c, d) R (e, f) $\Rightarrow$ (a, b) R (e, f) for all (a, b), (c, d), (e, f) $ϵ N \times N .$

Let R be a relation on N×N defined by (a,b)R,(c,d)⇔a+d=b+c for all (a,b),(c,d)ϵN×N Show that : (i) (a, b) R (a, b) for all (a,b)ϵN×N (ii) (a,b)R(c,d)⇒(c,d)R(a,b) for all (a,b),(c,d)ϵN×N (iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ϵN×N.

Answer»

Let R be a relation on $N \times N$ defined by $(a, b) R, (c, d) \Leftrightarrow a + d = b + c$ for all $(a, b), (c, d) ϵ N \times N$

Show that :

(i) (a, b) R (a, b) for all $(a, b) ϵ N \times N$

(ii) $(a, b) R (c, d) \Rightarrow (c, d) R (a, b)$ for all $(a, b), (c, d) ϵ N \times N$

(iii) (a, b) R (c, d) and (c, d) R (e, f) $\Rightarrow$ (a, b) R (e, f) for all (a, b), (c, d), (e, f) $ϵ N \times N .$