15. Let L/x y) be the propositional function "x loves y."The domain of discourse is the Cartesian product of the set of all living people with itself (i.e., both x and y take on values in the set of all living people). Write each proposition in Exercises 28-31 symbolically. Which do you think are true? a. Someone loves everybody. b. Everybody loves everybody. c. Somebody loves somebody. d. Everybody loves somebody. e. Write the negation of each proposition above in words and symbolically. 16. Draw the combinatorial and the switching circuit diagrams for the statement a. (pv q) (~r v (p ^ ~q)). 17. Determine whether the following argument is valid. Therefore