Answer the questions and explain the answers Section 1.5 Nested Quantifiers

Q10 Let F(x, y) be the statement x can fool y, where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) Everybody can fool Fred. b) Evelyn can fool everybody. c) Everybody can fool somebody. d) There is no one who can fool everybody. e) Everyone can be fooled by somebody. f ) No one can fool both Fred and Jerry. g) Nancy can fool exactly two people. h) There is exactly one person whom everybody can fool. i) No one can fool himself or herself. j) There is someone who can fool exactly one person besides himself or herself.

Q28 Determine the truth value of each of these statements if the domain of each variable consists of all real numbers a) xy(x2 = y) b) xy(x = y2) c) xy(xy = 0) d) xy(x + y y + x) e) x(x 0 y(xy = 1)) f ) xy(y 0 xy = 1) g) xy(x + y = 1) h) xy(x + 2y = 2 2x + 4y = 5) i) xy(x + y = 2 2x y = 1) j) xyz(z = (x + y)2)