Hi,
I was just going through Latch circuits worksheets. The link is given below.
http://www.allaboutcircuits.com/worksheets/latch.html

In question no.7, why cant we just use an x-or gate??
Can anybody explain to me the logic that has been used to control the motor?

 

xor would produce "1" when inputs are different. this means it would turn motor on regardless which button is pressed, as long as other button is off.

look at Q8 and Q9.