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Assume A is a wff (well formed formula). Give a proof by induction that in order to assign a truth value to A it suffices to assign truth values to variables occurring in A.
Provide a definition by recursion of a function F such that for every wff (well formed formula) A, F(A) is a wff (well formed formula) obtained from A by replacing all occurrences of p with q and all occurrences of q with p simultaneously. (For example, F((p implies q)) = (q implies p).)
Clear glass costs $3 per square foot and stained glass costs $10 per square foot. Express the cost of the window as a function of the radius of the stained glass pane.
A rectangular parcel of land has an area of 5000 ft^2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, rounded to the nearest foot?
If one ball is drawn at random, find the probability it is red. If two balls are drawn, find the probability both are green. If two balls are drawn, find the probability one is red and the other is blue
Let A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff m|n. Show that this relation is a partial ordering relation. Draw its Hasse diagram.
Your weekly paycheck is 20 percent less than your coworker's. Your two paychecks total 885. Find the amount of each paycheck.
One card will be randomly selected from a standard 52-card deck of cards. What is the probability that it will be the jack of hearts?
A 105 ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire ne..
You can operate a train if at least 200 people buy tickets. The fare will be $8 per person if 200 people buy tickets, but will decrease 1 cent for each additional person over 200. what number of passangers will bring the railroad the maximum reven..
Discrete random variable with probability mass function, 1) Let X be a discrete random variable with probability mass function Pr{X=k}= c/(1+(k^2)) for k= -2,-1, 0, 1, 2.
How much should he invest in each to maximize his return? Assume the investment returns are as expected.
the doubling period of a baterial population is 10 minutes. At time t=110 minutes, the baterial population was 90000.
At the same time, it is expected that 20% of those now using public transportation will commute via automobile, and 80% will continue to use public transportation. In the long run, what percentage of the commuters will be using public transportati..
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