12–
Quantifiers
For
problems 1-4 below, let L(x,y) be the propositional
function “x loves y.” The domain of
discourse, D, is the set of all
living people. Write each proposition symbolically. BTW, which do you think are
true?
1. Everybody loves everybody.
2. Somebody loves somebody.
3. Everybody loves somebody.
Write
the negation of problem 3 above in words and symbolically.
4.
Determine
the truth value for each statement. The domain of discourse is the set of real
numbers. Justify your answer.
5. For every x, x2 > x.
6. For some x, x2 > x.
7. For every x, if x > 1 then x2 > x.
8. For some x, if x > 1 then x2 > x.
9. For every x, for some y, x2 < y + 1.
10. For some x, for every y, x2 < y + 1.