1) Each problem consists of three statements, the first two statements are true and please select if the third statement is true, false or uncertain by using your logical reasoning skills. (10 Points) a) Bob is older than Alice. Alice is younger than Ted. Ted is older than Bob. A. True False Uncertain B. C. b) All trees in the park are flowering trees. Some of the trees in the park are Magnolia. All Magnolias in the park are flowering trees. A. True B. False C. Uncertain c) All of the offices on the 11 floor have wall-to-wall carpeting. No wall-to-wall carpeting is pink. None of the offices on the 11 floor has pink wall-to-wall carpeting. A. True False B. C. Uncertain 2) A and B are sets and they are defined below. Answer the following questions. (10 Points) U- {1, 2, 3, 4, 5, f, b, 9, 1, 0, j) A= (1, 3, 5, f, b, t, 0) B- (4, 5, 9, 1, 1) a) BIA is it true or false? b) A-B? c) B-A? d) A-U? A B? e) f) A B? g) BU? h) |B? i) B- (A B)? j) A-(A B)? k) A? DABU? m) ADB? 3) There are 307 students in a high school. 31 of them are taking Biology, Physics and Math at the same time. 60 students are taking Physics and Math, 54 are taking Physics and Biology, 79 are taking Biology and Math.144 students are taking Math, 113 are taking Physics, 108 are taking Biology. How many students does not take any of these courses? (Show your work) (10 Points) 4) Which of the following statement is a proposition? (10 Points) a) Where are you going? b) It is a sunny day. c) Your eyes are beautiful. d) God bless you! e) The only odd prime number is 2. 5) Which of the following option is true? (10 Points) a) If Jupiter is a planet, lions will fly b) 3+5 9 if 5-4-3 c) 2>5 and 5 is a positive integer d) -2