Prove the following theorems algebraically:

(a) x(x′ + y) = xy
(b) x + xy = x
(c) xy + xy′ = x
(d) (a + b)(a + b′) = a

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 33 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30 ∘c on monday, but decreased at a constant rate in the next 33 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.