Use conditional proof or indirect proof and the eighteen rules of inference to establish the truth of the following tautologies. P â£[P V(Q . ~ Q)]

Adepartment store purchases screen-printed t-shirts at a cost of $5 per shirt. they mark up the price 150% (making the selling price 250% of the store's purchase price) and put them on the sales floor. every month that a t-shirt doesn't sell, the store reduces the selling price by 25%.

Find the coordinates of point x that lies along the directed line segment from y(-8, 8) to t(-15, -13) and partitions the segment in the ratio of 5: 2.

Harry the hook has 7 1/3 pounds of cookie dough.she uses 3/5 of it to bake cookie. how much cookie dough does she use to make cookie?