1. Let A={a, b, {c, d}, e}. How many elements does A contain?
Correct : D. 4
2. Let A={2,{4,5},4} Which statement is correct?
Correct : C. {4, 5} is an element of A.
3. Which of these sets is finite?
Correct : C. {1, 2,
3,...,999,1000}
4. Which of these sets is not a null set?
Correct : B. B = {x | x + 10
= 10}
5. . Let S={1, 2, 3}. How many subsets does S contain?
Correct : C. 8
6. . Which set S does the power set 2S = {Ф,{1}, {2}, {3}, {1,
2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?
Correct : B. {1, 2, 3}
7. Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct?
Correct : A. A U B ={v, w,
x, y, z}
8. which sets are equal ? 1.{r,s,t} 2.{s,s,t,r} 3.{t,r,t,s}
Correct : D. all are equal
9. A U A=A according to …….law
Correct : C. Indempotent law
10. In any application of the theory of sets, the members of all the sets belongs to …… set
Correct : C. universal
11. let A={{a,b}} then aЄ A
Correct : B. FALSE
12. ФЄФ
Correct : B. FALSE
13. The sets {a,b,c} and {b,c,a} represnet the same sets.
Correct : A. TRUE
14. Cardinality of a set is number of element of the set.
Correct : A. TRUE
15. Multiset is an unordered collection of elemnts where an element can occur a a member more than once
Correct : A. TRUE
16. one of the A or B is uncountably infinite and one is countably infinite then | AUB| will be
Correct : D. uncountably infinite
17. Sum of first n positive integers is
Correct : C. n(n+1)0.5
18. Let P(S) denote the power set of set S. which of the is always true
Correct : C. P(S)∩P(P(S))
={Ф}
19. {3}Є{1,3,5}
Correct : B. FALSE
20. consider the following data for 120 mathematics students at a college concerning the languages French,Gernan, and russian: 65 study frensh, 45 study german 42 study russian , 20 study french and german, 25 study french and russian, 15 study german and russian. 8 study all three languages. Determine how many students study exactly 1 subject?
Correct : C. 56
21. ……… is an unordered collection of elements where an element can occur as a member more than once
Correct : A. Multiset
22. In a room containing 28 females, there are 18 females who speak English, 15 females speak french and 22 speak german. 9 females speak both english and french, 11 females speak both french and german where as 13 speak both german and english. How many females speak all 3 languages?
Correct : D. 6
23. If U = {1, 2, 3, . . . 10 } and S = { 4, 5, 6, 7, 8 }, then S ' =
Correct : D. {1, 2, 3 9 10 }
24. If U = {1, 2, 3, . . . 20 } and S = set of prime numbers , then S =
Correct : B. { 2, 3, 5, 7, 11,
13, 17, 19 }
25. Consider the statement,“If n is divisible by 30 then n is divisible by 2 and by 3 and
by 5.”Which of the following statements is equivalent to this statement?
Correct : D. If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30
26. Which of the following statements is the contrapositive of the statement, “You win the
game if you know the rules but are not overconfident.”
Correct : A. If you lose the game then you don’t know the rules or you are overconfident.
27. A sufficient condition that a triangle T be a right triangle is that a2 + b2 = c2. An equivalent statement is
Correct : B. If a2 + b2 = c2 then T is a right triangle.
28. Which of the following is the inverse of the statement: " If I eat a mango than I do not drink milk".
Correct : B. If I don’t eat a mango then I drink milk
29. If p= It is hot, and q= It is sultry, which of the following sentences in the appropriate version for the symbolic expression: -p٨ q
Correct : D. None
30. which of the following is the contrapositive of the statement: " A quadrilateral is a square only if it is both rectangle and a rhombus".
Correct : C. If a quadrilateral is neither a rectangle nor a rhombus then it is not a square
31. For a conditional statement p===>q, which of the following is incorrect.
Correct : D. None
32. Which of the following is equivalent to p==>q
Correct : C. ~xpVq
33. Equivalent inverse of p==>q is
Correct : D. pV~q
34. Converse of p==>q is
Correct : D. pV~q
35. the truth table for exclusive disjunction will be
Correct : D. p or q but not both
36. The conditional statement p→q and its contrapositive are….
Correct : C. Logically equivalent
37. Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is ….
Correct : B. 6
38. Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is ….
Correct : B. 9
39. if P∩ Q= Ф then P U Q' is
Correct : C. U-Q
40. The number of proper subset of {1,2,3,4} is
Correct : A. 16
41. Consider the four statements: 1.(q==>p)٨(~p) 2. p==>(~q) V r 3. ~p==>~(p٨q)
4.p٨q٨~(pVq) Which one is tautology.
Correct : C. C
42. Which among the statements given in Q.70 is contradiction
Correct : D. D
43. Consider the four statements 1.p٨~q↔~p V q 2.p٨(~p Vq)٨(~q) 3.(pV(~q))٨ ~((~p)Vq) 4.~(p↔q)↔(p↔~q) which one of this contradiction.
Correct : D. D
44. consider the four tsatements: 1.(p→q) ٨(p٨~q) 2.(~p→r)٨(p↔q) 3.p→(~qVr) 4.~(p٨q) V (p↔q) Which one of these four ststements is a tautology.
Correct : D. D
45. In above question which statement is contradiction.
Correct : A. A
46. Which of the following sets are equal. 1. {p,q,m,n} 2.{m,p,n,q} 3.{q,p,p,m,m,p,n} 4.{p,q,n,,n,m}
Correct : D. All are equal.
47. Consider the set A={{1,3,5},{7,9,11},{13,15}} then determine which of the following is/are true.
1.1ЄA 2.{{1,3,5}} CA 3. Ф subet of A 4. A
Correct : A. 2 and 3 is true
48. Determine the validity of the following argument: S1: all my friends are musicians. S2: John is my friend. S3: None of my neighbours are musicians. S: John is not my neighbour.
Correct : A. Valid
49. In a survey of 60 people , it was found that: 25 read Newsweek magzine. 26 read Time 26 read Fortune 9 read both newsweek and fortune 11 read both Newsweek and Time 8 read both Time and Fortune 3 read all 3 magzines. 1. Find the number of people who read at least one of the three magzines
Correct : B. 52
50. In above Q.78 Find the number of people who read exactly 1 magzine.
Correct : A. 30
51. In a class of 80 students , 50 students know English, 55 know french and 46 know german language. 37 students know english and french, 28 students know french and german, 7 students know none of the languages. Find out how many students know all the three languages?
Correct : A. 73
52. In above q.80 how many students exactly know 2 languages?
Correct : B. 54
53. In q. 80 how many students know exactly 1 language?
Correct : C. 7
54. A preposition is a statement that is either ture or false
Correct : A. TRUE
55. A prepostition that is true under all circumstances is referred to as a ….
Correct : A. Tautology
56. A prepostition that is false under all circumstances is referred to as a ….
Correct : B. Contradiction
57. p→q is logically equivalent to ~p V q according to…
Correct : B. Implication law
58. A logical expression which consist of a product of elementary sum is caleed…..
Correct : B. Conjunctive normal form
59. A logical expression which consist of a sum of product is caleed…..
Correct : A. Disjunctive normal form
60. An assertion that contains one or more variable is called a….
Correct : C. Predicates
61. Determine the validity of argument given: s1: If I like mathematics then I will study. S2: Either I will study or I will fail. S: If I fail then I do not mlike mathematics.
Correct : B. Invalid
62. p V ~(p٨q) is….
Correct : B. Tautology
63. Determine the validity of the argument s1: If I stay up late at night , then I will be tired in the morning. S2: I stayed up last last night s: I am tired this morning.
Correct : A. Valid
64. An argument is valid if, whenever the conclusion is true, thenthe premises are also true.
Correct : B. FALSE
65. De Morgan's laaws are two examplesof rules of inference
Correct : B. FALSE
66. In a club , all members participate either in tambola or the fete. 420 participate in the fete, 350 play tambola and 220 participate in both. How many members does the club have?
Correct : B. 550
67. dual of (p V q)٨ r is..
Correct : B. (p٨q) Vr
68. It was found that in first year of computer science of 80 students 50 know Cobol, 55 know C, 46 know pascal. It was also known that 37 know C and cobol, 28 know C and pascal , 25 know pascal and cobol, 7 students know none of the languages. Find how many all the 3 languages?
Correct : B. 12
69. In above q.97 How many know exactly 2 languages?
Correct : A. 54
70. In q.97. How many know exactly 1 language?
Correct : C. 7
71. In the class of 55 students the number ofstudying different subjects are as given below: Maths 23, Physics 24, chemistry 19, maths+physics 12, maths+chemistry 9, Physics +chemistry 7, all three subjects 4. Find the number of students who have taken atleast 1 subject?
Correct : C. 42
72. [~ q ^ (p→q)]→~ p is,
Correct : B. tautology
73. If P and Q stands for the statement P : It is hot
Q : It is humid,
then what does the following mean? P Ù (~ Q):
Correct : B. It is hot and it is not humid
74. In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea.Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like none of the three drinks. Find the number of people who like all the three drinks.
Correct : C. 8
75. The statement ( p^q) → p is a
Correct : C. tautology
76. Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome” is:
Correct : B. ~ (~ p ^q)
77. Let P(S) denotes the powerset of set S. Which of the following is always true?
Correct : D. S € P(S)
78. Which of the following proposition is a tautology?
Correct : C. p v (p→q)
79. Which of the following statement is the negation of the statement “4 is even or -5 is negative”?
Correct : A. 4 is odd and -5 is not negative
80. Which one is the contrapositive of q → p ?
Correct : B. ~p →~q
81. Check the validity of the following argument :- “If the labour market is perfect then the wages of all persons in a particular employment
will be equal. But it is always the case that wages for such persons are not equal
therefore the labour market is not perfect.”
Correct : B. Valid
82. ∃ is used in predicate calculus
to indicate that a predicate is true for all members of a
specified set.
Correct : A. TRUE
83. ∀ is used in predicate calculus
to indicate that a predicate is true for at least one
member of a specified set.
Correct : A. TRUE
84. “If the sky is cloudy then it will rain and it will not rain”
Correct : C. tautology
85. Represent statement into predicate calculus forms : "Not all birds can fly". Let us assume the following predicates bird(x): “x is bird” fly(x): “x can fly”.
Correct : B. ∃x bird(x) ^ ~
fly(x)
86. Represent statement into predicate calculus forms : "If x is a man, then x is a giant." Let us assume the following predicates
man(x): “x is Man” giant(x): “x is giant”.
Correct : C. ∀ (man(x)→
giant(x))
87. Represent statement into predicate calculus forms : "Some men are not giants." Let us assume the following predicates
man(x): “x is Man” giant(x): “x is giant”.
Correct : B. ∃x man(x) ^
~ giant(x)
88. Represent statement into predicate calculus forms : There is a student who likes mathematics but not history. Let us assume the following predicates student(x): “x is student.”
likes(x, y): “x likes y”. and ~likes(x, y) “x does not like y”.
93. Test the validity of argument:“If it rains tomorrow, I will carry my umbrella, if its cloth is mended. It will rain tomorrow and the cloth will not be mended. Therefore I will not carry my umbrella”
Correct : B. Valid
94. In a group of athletic teams in a certain institute, 21 are in the basket ball team, 26 in the hockey team, 29 in the foot ball team. If 14 play hockey and basketball, 12 play foot ball and basket ball, 15 play hockey and foot ball, 8 play all the three games. (i) How many players are there in all?
Correct : D. 43
95. In above Q.123 (ii) How many play only foot ball?
Correct : A. 10
96. (p ↔ q) ↔ r = p ↔ (q ↔ r)
Correct : C. tautology
97. Write the negation in good english sentence : "Jack did not eat fat, but he did eat broccoli."
Correct : B. If Jack did not eat broccoli then he did ate fat.
98. Write the negation in good english sentence : The weather is bad and I will not go to work.
Correct : A. The weather is not bad or I will go to work.
99. Write the negation in good english sentence : Mary lost her lamb or the wolf ate the lamb.
Correct : C. Mary did not loss her lamb and the wolf did not eat the lamb.
100. Write the negation in good english sentence : I will not win the game or I will not enter the contest.
Correct : B. I will win the game and I will enter the contest.