The are 99 dogs. 49 bark consistently while 69 whines. 29 dogs both whine and bark. How many of the dogs neither whine nor bark?
Best illustrated with a Venn diagram.
Draw two intersecting circles, label one barking, the other whining.
place 29 in the intersection of the two circles
In the non-intersecting part of the barking circle place 49-29 or 20
In the non-intersecting part of the whining circle place 69-29 or 40
Add the numbers you see in your circles:
40+29+20 = 89
but you had 99 dogs, so 10 would not be in either the barking or whining circles
- they neither bark nor whine
or
Number(bark or whine) = number(bark) + number(whine) - number(bark AND whine)
= 49+69-29 = 89
leaving 10 not accounted for.