2. (30 pts) Write a program that produces the truth table for the following compound propositions. Write the header(s) of the table(s), including intermediate steps and the final result. Output the result on the file_prog2 output.txt. (e) (p-> q) (neg q > neg p) (f) (p or q) and neg (p and q) (h) p and neg p Note: 1. Examples of output.txt files are on the Blackboard. Check slides for an example writing on a.txt file. this week's in-class assignment solution that does the trick. predefined in C++. 2. The table should contain the letters 'T' and'F', it should not print 1s and Os. Check 3. Do NOT hard code the truth tables. Your program must use the logical operators 4. For t the conditional (-) and biconditional >),you can use the logical equivalences (See Table 7 and Table 8 in slides or the textbook) to calculate the truth tables. 5. For Problem 2 (e), a good way to solve it is to first define, in Problem 1, your own "conditional" and "biconditional" operators as C++ functions, using the logical equivalences mentioned above, then call them in Problem 2 (e)