1. simplify the following expressions using boolean algebra.
a. y = (q + r)(q' + r')
b. w = abc + ab'c + a'
c. q = (rst)' (r+s +t)'
d. x = a'b'c'+ a'bc + abc + ab'c' + ab'c
e. z = (b+c')(b'+c) + (a'+b+c')'
y = (c+d)' +a'cd' + ab'c' + a'b'cd + acd'
g. x = ab(c'd)' + a' bd + b'c'd'
h. z = [ab'(c + bd) + a'b']c

What a backup plan that you have created in a event you encounter a situation

The average cost of one year at a private college in 2012-2013 is $43,289. the average grant aid received by a student at a private college in 2012-2013 is $15,680.   what is the average student contribution for one year at a private college in 2012-2013?

Me with this program in c++ ! computers represent color by combining sub-colors red, green, and blue (rgb). each sub-color's value can range from 0 to 255. thus (255, 0, 0) is bright red. (130, 0, 130) is a medium purple. (0, 0, 0) is black, (255, 255, 255) is white, and (40, 40, 40) is a dark gray. (130, 50, 130) is a faded purple, due to the (50, 50, 50) gray part. (in other word, equal amounts of red, green, blue yield gray).given values for red, green, and blue, remove the gray part. ex: if the input is 130 50 130, the output is: 80 0 80. thus, find the smallest value, and then subtract it from all three values, thus removing the gray.