Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: December 2015

Let S={1, 2, 3, 4, 5} and A=S×S. Define the following relation R on A: (a,b) R(c,d) if and only if ad=bc show that R is an equivalence relation and compute A/R.

Lets S={1,2,3,4,5}, A=SxS

R=(a,b)R(c,d) if ad=bc

Let (a,b) R (a,b) ∴ ab=ba

This expression is true, hence (a,b) R (a,b)

∴ Given relation Is reflexive. It (a, b) R (c, d) ∴ ad =bc ...(i)

Then check for (c, d) R (a, b) ∴ cb=da

Above two expression are similar …