Mathematics IT (Discrete Structures)

Question

For items 31 – 34. Fill in the blanks with word to complete the statement.

a. Negation                     b. Tautology            c. Aristotle        d. Premise

31. The father of logic is ______. 

32.The truth value of the _______ of a statement is always the reverse of the truth value of the original

statement.  

33.P→Q is the symbol for “if P then Q”. P is called _____.

34.It is a compound statement that is true for all possible combinations of the truth values of the propositional variables.  

35.A logical connective symbol for “and”.     a. ⊕           b. ∧            c. ∨       d. →

36.A logical connective symbol for “or”.     a. ⊕           b. ∧            c. ∨       d. →

37.The following are the logical connectives except __.

a. Conjunction     b. Conditional     c. Bijection         d. Disjunction

For items 38-42

Determine the truth value for the following given statements

a.True         b. False

38. If 2 +3 = 5 is sufficiently condition for 5 – 2 = 1.              

39.Snakes are reptiles and dogs are mammals.                         

40.Indonesia is the largest archipelago or 2 + 3 = 5.               

41.Philippines is a republican country if 18 is less than 20.     

42.Intel is a processor if and only if Mars is a red planet.        

43.Hongkong is the capital of China is equivalent to fish live in dry land.

For items 44-45

Given:  ~ (P ↔ Q) ∨ ~ P T F T F

44.Determine the truth table.      a.  T                                   b.   T                  c.    F                     d. F

F T T F

F T F T

45.Which of the ff. is the truth table classification?  a. Tautology  b. Contradiction  c. Contingency 

46. “IF JOSE LEARNS LOGIC WELL, THEN HE WILL UNDERSTAND BOOLEAN ALGEBRA”.    Meanwhile, “IF JOSE DOES NOT LEARN LOGIC WELL, THEN HE WILL NOT UNDERSTAND BOOLEAN ALGEBRA” is known as___.

a. Converse       b. Inverse       c. Contrapositive     d. none of these

For items 47 – 50. Fill in the blanks with rule of inference.

a.Modus Ponens  b. Modus Tollens    c. Rule of Disjunctive Syllogism       d.  Law of Syllogism

47. If 24 is divisible by 12, then 12 is divisible by 3. If 12 is divisible by 3, then 24 is divisible by 3. Therefore, if 24 is divisible by 12, then 24 is divisible by 3. _______

48.If the promises of elected official are fulfilled, then development in his jurisdiction is observed. Development in elected official’s jurisdiction is not observed. Therefore, the promises of elected official are not fulfilled._________

49.Hardworking student gets passing grades. If hardworking student gets passing grades, then he will pursue his education. Therefore, hardworking student will pursue his education.__________

50.10 > 3 OR 5 ≤ 2. 10 ≤ 3. Therefore, 5 ≤ 2.  __________

For items 51 – 54. Fill in the blanks with word to complete the statement.

a.Boolean Algebra     b. Logic Gate      c. NOT Gate           d. Boolean Function

51. __________is an elementary building block of a digital circuit.

52.__________set out the basic principles of logic.

53.__________ refers to logical operations on one or more logic inputs and produces a single logic output.

54.__________ is also known as logical inverter.

For items 55-58. Construct the Boolean function through truth table.

0 0 1 1

a. 1               b.  1                     c.  1               d.  0                            

1 0 0 1

1 1 1 1

55. f (x,y) = (x+y) ⊕ x’  

56. f (x, y) = x’ + y’         

57. f (x, y) = (xy)’ • y’    

58. f (x,y) = (x⊕y)’ + y  

Answer 1

33. Premise

34. B

33. C

34. B

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