P={p_1, p_2, p_m}, the set of products available at a local grocery store;
d={t_1, t_2, t_n}, the set of transactions that were completed at this store in the past year, where each t_i (i in [1,n]) is a subset of p;
min_freq, a user-specified parameter (e. g., 5%).
a product is said to be frequent if it occurs in at least min_freq of the transactions in d. by the same token, a pair of products is said to be frequent if it occurs in at least min_freq of the transactions in d. also, it's straightforward to prove the following claim: if a product is not frequent, none of the pairs that involve this product will be frequent. use this claim to design an algorithm to find all the frequent products and frequent product pairs in d. represent your algorithm in pseudo code.

Write a program that uses a widgetviewer object to do the following: generate two random integers between 1 and 9 (inclusive). name one of them x, the other y. display them to the user using jlabel objects. create a jlabel object displaying the text "enter an operation number." create a jtextfield for the user's input. create a jbutton displaying the text "press here when you've entered your operation." use addandwait to add it to the widgetviewer object. when the user clicks the jbutton, evaluate operation in the following order to determine the one and only mathematical operation to perform on x and y. use a jlabel to display the result. if operation is between 1 and 10 inclusive, add x and y. if operation is evenly divisible by 4, subtract y from x. if operation is evenly divisible by 5, use integer division to divide y into x. if operation is an even number, use floating point division to divide y into x. if none of the other tests on operation apply, multiply x and y. note: operation can be negative or zero.

Create a cell reference in a formula by typing in the cell name or         a. right-clicking the cell. b. clicking the cell. c. clicking the column where the cell is located. d. clicking the row where the cell is located.

Many everyday occurrences can be represented as a binary bit. for example, a door is open or closed, the stove is on or off, and the fog is asleep or awake. could relationships be represented as a binary value? give example.