Let K (x) denote the statement \"x\" has programmed with LISP\" and D denote the
ID: 3850058 • Letter: L
Question
Let K (x) denote the statement "x" has programmed with LISP" and D denote the domain of all students in our class. Express each of these quantified propositions in English: (a) _x elementof D: K(x) (b) not Forall_x elementof D: K(x) (c) Forall_x elementof D: not K(x) Let Q(x) denote the statement "x^2 > 3x" and Z denote all integers (i.e., ., -3, -2, -1, 0, 1, 2, 3, .). Determine the truth value of each of these statements: (a) Q(2) (b) 2(4) (c) Forall_x elementof Z: Q (x) (d) _x elementof Z: not Q(x) Translate the following statements to English where C (x) is "x is a computer scientist" and M(x) is "x has taken discrete math" and the domain D is all students at UTSA. (a) Forall_x elementof D: (M (x) rightarrow C(x)) (b) Forall_x elementof D: C(x) M(x) (c) _x elementof D: not C (x) Lambda M (x)Explanation / Answer
Solution :
1)
a) solution 1 : There is at least one student in class who has programmed with LISP.
solution 2 : there exist a student in class who has programmed with LISP.
b) solution 1 : It is not true that, all studnets in class has programmed with LISP.
solution 2 : Not all students in class has programmed with LISP.
solution 3 : There is at least one student in class who has not programmed with LISP.
c) solution 1 : None of the student in class has programmed with LISP.
2)
a) Q(2) :
here 2^2 is less than 3*2 . hence Q(2) is false.
b) Q(4) :
here 4^2 is greater than 3*4. Hence Q(4) is true.
c) Given statement : Q(x) is true for all value of x is Z.
Q(x) is not true for x = 2.
Hence there is some value of x in Z for which Q(x) is not true.
hence, statement "Q(x) is true for all value of x is Z" is false.
3)
a) solution 1 :If a student of UTSA has taken discrete math then he is a computer scientist.
solution 2 : If a person is student at UTSA and he/she has taken discrete math then he/she is a computer scientist.
b) solution 1 : All students of UTSA has taken discrete math or is computer scientist.
solution 2 : Any Student of UTSA has taken discrete math or is a computer scientist.
c) solution 1 : There is at least one student at UTSA who is not computer scientist and has taken discrete math.
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