Question: please answer all questions thank you 1. Given a proposition p, which of the following is a tautologr: a. pAp b. p c. pV d.

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1. Given a proposition p, which of the following is a tautologr: a. pAp b. p c. pV d. D 2. A student makes a claim that "there exist at least 2 people in the world who have the same birthday". Peter offers the following argument as proot: "Since there are over 7 billion peopie in the world and only 365 days in a yeac, there must be at least 2 people in the world who have the same birthday". Which of the following describes Peter's proof: a. is a constructive proof b. It is a non-constructive proof c. It is a proof by induction d. It is a proef by contraposition 3. Which of the following statements is not a proposition a. The moon is made of green cheese b. The New Orleans Saints won the 2022 Super bowl c. Don't drink and drive d. Muhammad Ali is the greatest boxer af all time, and Louiville Kentucky is the greatest city of all time. 1 4. Given the condaional, pq. Which of the following is its inverse a. qp b. qp c. q d. 1/p1/q 5. Determine the truth value of the following statement if the domain consiats of all integers: n3m(n+m=0) a. True b. False. c. Indeterminate d. Not a propesition 6. Given a propositional function 3(x) denoting " x has taken a course in Java", and a domain consisting of all students in the class, translate the following sentence into predicate logic: "Every rudent in this class has taken a course in Java." a. 3x(x) b. Val(x) c. 3xx(x)x) d. vx3x.f(x) 7. Given the domain, U= (ffeegles, stoows, thingamabobs), and the propositional functions F(x):x is a fleegle s(x): x is a stoow T(x):x is a thingamabob The task is to convert the following English statement into a logical expression: "If a fleege is a stoow then it is also a thingamabob: " Which of the following is the correct convetsion: a. vx((F(x)5(x))T(x)) b. x(F(x)T(x)S(x)) c. 3x(F(x)T(x)) d. x((F(x)S(x))T(x))

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