Question

kindly solve it and show all the work here as i think its not too difficult do it as soon as possible

11. (5 points) Given a quantified statement VxP(x) for some domain of x. Suppose you believe that statement is incorrect. How do you prove it? Explain 12. (5 points) Let S(x) be the predicate "x is a student", F(x) the predicate "x is a faculty member" and A(x, y) predicate "r has askedy a question" where the domain consists of all people associated with the school. Use quantifiers to express this statement: "Some faculty member has asked every other faculty member a question." 13. (1 point) The inverse of the function f(x)= 1/x over the domain of real numbers is an onto function A. True B. False n/2]n/2 14. (5 points) Consider the sequence defined by an Give the terms ao, aj, a2, a3, a4. +

Answer 1

11) To prove this wrong I need to prove the following statement:

3.1 P(1)

Which means that I need to find an x from the domain that support the negation of P(x)

12) The correct representation of the given statement would be:

3.0F (2) VyF(y),A(1,)

13) It would be false, because at 0, the function diverges. Hence the answer is B

14) Observe that

n = 2k = n/2 = (n/21 = k an=n n=2k +1 = n/2] = k, [n/2] = k +1 an = k + k + 1) = n

Hence the terms would be 0,1,2,3,4