Task Performance (discrete).docx

TASK PERFORMANCE DISCRETE STRUCTURES

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Submitted to: Ma’am Vivian Gay Ordoño

EXERCISES B. Let T(x, y) be the propositional function “x is taller than y.” The domain of discourse consists of three students: Garth, who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marty who is 6 feet tall. Write each proposition in Exercises 12-15 in words and tell whether it is true or false. Proposition in Words

Truth Value

12. 13. 14. 15.

16. Write the negation of each proposition in exercises 12-15 in words and symbolically.

C. Let L(x, y) be the propositional function “x loves y”. The domain of discourse is the set of all living people. Write each proposition in exercises 17-20 symbolically. Which do you think are true? Proposition in Words 17. 18. 19. 20.

21. Write the negation of each proposition in exercises 17-20 in words and symbolically

Truth Value

D. Determine the truth value of each statement in exercises 22-36. The domain of discourse is the sets of real numbers. Justify your answers. 22. For every x, x2 > x.

23. For some x, x2 > x.

24. For every x, if x > 1, then x2 > x.

25. For some x, if x > 1, then x2 > x.

26. For every x, if x > 1, then x / (x2+1) < 1.

27. For some x, , if x > 1, then x / (x2+1) < 1.

28. For every x, for every y, x2 < y+1.

29. For every x, for some y, x2 < y+1.

30. For some x, for every y, x2 < y+1.

31. For some x, for some y, x2 < y+1.

32. For some y, for every x, x2 < y+1.

33. For every y, for some x, x2 < y+1.

34. For every x, for every y, x2 + y2 = 9.

35. For every x, for some y, x2 + y2 = 9.

36. For some x, for every y, x2 + y2 = 9.

Problems in Set 1. The career preferences of a group of 60 college students were recorded as follows: 30 students prefer careers in engineering 40 prefer science related careers 35 prefer medical careers 20 would like to consider career in both engineering and sciences 25 would like to consider career in both science and medicine 18 would like to consider career in both engineering and medicine 10 would consider all these three career paths

Using the Venn diagram, the following additional results from the survey can be easily verified a. The number of students who do not like any of the three careers

b. The number of students who prefer medicine only

c. The number of students who prefer exactly one of the three careers

d. The number of students who prefer exactly two of the three careers

e. The number of students who do not like medicine

2. There are three students organization (A, B and C) in a school. 50 students were asked if the belong to any of these organizations, and the following data were gathered from a survey: 7 belong to B only 20 belong to C 23 belong to A 5 belong to A and B but not to C 8 belong to A and C but not to B 14 belong to C but not to B 15 belong to A but not to B

Draw a Venn diagram to determine how many of the students surveyed a. belong to C only

b. belong to A only

c. do not belong to C

d. do not belong to B

e. belong to B and C but not A

f. belong to exactly one organization

g. do not belong to any of those organization

4. The 300 workers of a certain company have just negotiated a new contract with the management whereby additional funds will be contributed to employee benefit program. The employee’s were polled as to how the funds should be spent: 105 wanted better pension benefits 100 wanted better health benefits 120 wanted better dental insurance 35 wanted better pension and health benefits 40 wanted better dental insurance and health benefits 50 wanted better pension and dental benefits 20 wanted better pension, health and dental benefits

Determine of means of a Venn diagram the number of employees a. who wanted only a better pension plan

b. who wanted only a better dental plan

c. who wanted a better health and dental plan but were not interested in a pension benefit

d. who wanted a better health and pension plans only

e. who were not interested in any of these programs