If A - B =x and B - A =y , then what is ( A - B ) equal to?

Step-by-step solution

aligned & A - B =x & ~A ~A - B B =x & ( ~A - B ) A B =x aligned ( A - B )=x ~A ~B (i) aligned & B - A =y & ~B ~B - A A =y aligned ( A - B )=y ~A ~B ...(ii) From (i) and (ii) x ~A ~B =y ~A ~B aligned & ( A - B )= ( A - B ) ( A - B ) &= A B + A B x ~A ~B & [ x ~A ~B =y ~A ~B ] aligned aligned & = 1 x + A B x ~A ~B & = 1 x + A B y ~A ~B & = 1 x + 1 y aligned