Homework 1
Homework 3
by
Asif Subhan
2175 002
1/31/2013
4. State the value of x after the statement if P(x) then x := 1 is executed, where P(x) is the statement “x > 1,” if the value of x when this statement is reached is a. x=0 i. x is equal to zero, the condition is false. b. x=1 ii. x is equal to one, the condition is false. c. x=2 iii. x is equal to two, the condition is true. So the statement x: = 1 is executed. 6. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a. ∃xN(x) i. There exists a student in school, who has visited North Dakota. b. ∀xN(x) ii. All students in the school have visited North Dakota c. ¬∃xN(x) iii. There does NOT exist a student in the school who has visited North Dakota d. ∃x¬N(x) iv. There exists a student in school, who has NOT visited North Dakota. e. ¬∀xN(x) v. Not all students in the school have visited North Dakota. f. ∀x¬N(x) vi. All students in the school have NOT visited North Dakota. (no student has visited North Dakota) 10. Let C(x) be the statement “x has a cat,” let D(x) be the statement “x has a dog,” and let F(x) be the statement “x has a ferret.” Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a. A student in your class has a cat, a dog, and a ferret. i. ∃x(C(x) ∧ D(x) ∧ F(x)) b. All students in your class have a cat, a dog, or a ferret. ii. ∀x(C(x) ∨ D(x) ∨ F(x)) c. Some student in your class has a cat and a ferret, but not a dog. iii. ∃x(C(x) ∧ F(x)∧¬D(x)) d. No student in your class has a cat, a dog, and a ferret. iv. ¬∃x(C(x) ∧ D(x) ∧ F(x)) e. For each of
by
Asif Subhan
2175 002
1/31/2013
4. State the value of x after the statement if P(x) then x := 1 is executed, where P(x) is the statement “x > 1,” if the value of x when this statement is reached is a. x=0 i. x is equal to zero, the condition is false. b. x=1 ii. x is equal to one, the condition is false. c. x=2 iii. x is equal to two, the condition is true. So the statement x: = 1 is executed. 6. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a. ∃xN(x) i. There exists a student in school, who has visited North Dakota. b. ∀xN(x) ii. All students in the school have visited North Dakota c. ¬∃xN(x) iii. There does NOT exist a student in the school who has visited North Dakota d. ∃x¬N(x) iv. There exists a student in school, who has NOT visited North Dakota. e. ¬∀xN(x) v. Not all students in the school have visited North Dakota. f. ∀x¬N(x) vi. All students in the school have NOT visited North Dakota. (no student has visited North Dakota) 10. Let C(x) be the statement “x has a cat,” let D(x) be the statement “x has a dog,” and let F(x) be the statement “x has a ferret.” Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a. A student in your class has a cat, a dog, and a ferret. i. ∃x(C(x) ∧ D(x) ∧ F(x)) b. All students in your class have a cat, a dog, or a ferret. ii. ∀x(C(x) ∨ D(x) ∨ F(x)) c. Some student in your class has a cat and a ferret, but not a dog. iii. ∃x(C(x) ∧ F(x)∧¬D(x)) d. No student in your class has a cat, a dog, and a ferret. iv. ¬∃x(C(x) ∧ D(x) ∧ F(x)) e. For each of