1. Write a negation for each statement in the following
 a. Sets A and B do not have any points in common. 

b. Towns P and Q are not connected by any road on the map.

2. In the following determine whether the proposed negation is correct. If it is not, write a correct negation.

Statement: The product of any irrational number and any rational number is irrational.
Proposed negation: The product of any irrational number and any rational number is rational.

3.  write a negation for the statement 18 and 19

4. the statements in the following refers to the tarski world explain why its true

For every square x there is a circle y such that x and y have different colors and y is above x.

5. Let C be the set of cities in the world, let N be the set of nations in the world, and let P(c, n) be “c is the capital city of n.” Determine the truth values of the following statements.

a. P(Tokyo,Japan)  c. P(Paris, France)

b. P(Athens,Egypt)  d. P(Miami, Brazil)

U, 18. Vx E R, if x(x+ 1) > 0 then x> 0 or x