Please refer to the image here. ?
1 Answer
Mar 10, 2017
# n(P' nn Q) = 22-x #
# n(P nn Q) \ \ = 13+x #
# n(P nn Q') = 15-x #
Explanation:
Using just set theory we have:
We are given
And,
Part (i);
# n(P' nn Q)+n(P)+x=n(epsilon) #
# :. n(P' nn Q)+28+x=50 #
# :. n(P' nn Q)=22-x #
Part (ii);
# n(P uu Q)=n(P)+n(Q)-n(P nn Q) #
# :. 50-x=28+35-n(P nn Q) #
# :. n(P nn Q)=13+x #
Part (iii);
# n(P nn Q')+n(Q)+x=n(epsilon) #
# :. n(P nn Q')+35+x=50 #
# :. n(P nn Q')=15-x #
Part (iv): Range
The min value for each of the above is 0;
# n(P' nn Q')=x ge 0 \ \ \ \ \ \ \ \ => x ge 0#
# n(P' nn Q) \ = 22-x ge 0 => x le 22 #
# n(P nn Q) \ \ \ = 13+x ge 0 => 13 +x ge -13 #
# n(P nn Q') \ = 15-x ge 0 => x le 15 #
Combining we get