3. Write the statements in symbolic form. Let p: The chili is spicy, g: The sour cream is cold. The sour cream is not cold if and only if the chili is spicy. Ans: If the chili is spicy, then the sour cream is not cold. Ans: Neither is the chili spicy nor is the sour cream cold. Ans: It is false that if the sour cream is not cold then the chili is spicy. Ans:

ii. Let F(x,y) be the open sentence "x can fool y" where the domain of discourse is the set of all people in the world. Express each of these statements using logical quantifiers. c. Everybody can fool somebody. e. Everyone can be fooled by somebody. f. There is somebody who can be fooled by everybody.

Consider the statement: If S = Ø then P(S) = Ø. (a) Is the statement true or false? (b) State the contrapositive. Is it true or false? (c) State the converse. Is it true or false? (d) State the contrapositive of the converse. Is it true or false? (e) Consider the statement: If S = Ø then P(S) ‡ Ø. Is this statement true or false? Is this statement equivalent to any of the statements above?

Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write INVALID