Question

if a={a, b},b={x, y},c={a, c, y} find (b-c)xa=(bxa)-(cxa)​

Answer 1

Step-by-step explanation:

( b-c ) = { x, y } - { a, c, y }

( b-c ) = {x}

(b-c)×a = {x} × {a, b}

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

Now,

b×a= {x,y} × {a,b}

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

c×a= {a,c,y} × {a,b}

= {(a,a) , (a,b) , (c,a) , (c,b) , (y,a) , (y,b)}

(b×a)-(c×a)= {(x,a) , (x,b) , (y,a) , (y,b)} - {(a,a) , (a,b) ,

(c,a) , (c,b) , (y,a) , (y,b)}

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

Therefore, (b-c)×a = (b×a)-(c×a)