CIS 125

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.