suppose R and S are relations from A to B then provedisprove

suppose R and S are relations from A to B then prove/disprove (R intersect S)^-1 = R^-1 intersect S^-1

Solution

let\'s assume R has a relation

firstly find left side

R={(a,b) (c,d)}

S={(x,y) (a,b)}

Now, we find intersection

R intersect S = {(a,b)}

(R intersect S)^-1 = {(b,a)}

Right side:

R^-1 = {(b,a) (d,c)}

S^-1 = {(y,x) (b,a)}

R^-1 intersect S^-1 = {(b,a)}

We can see that both sides are equal to (b,a)

Hence, this R intersect S)^-1 = R^-1 intersect S^-1 is correct.........Answer