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# Boolean algebra

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### Transcript of "Boolean algebra"

1. 1. Note: Please read the Important Instructions and Disclaimer file beforesolving the MCQs Boolean Algebra1) The negative of q v ~ (p ^ r) is A) ~ q ^ (p ^ r) B) ~ ^ (p ^ r) is C) ~ q v (p ^ r) D) ~ q v (p ^ r)2) The proposition (p  ~ p) ^ (~ p ~ p ) is a: A) Tautology and contradiction B) Neither tautology nor contradiction C) Contradiction D) Tautology3) Which of the following is always true? A) (p  p)  ~ q  ~ p B) ~ (p v q)  v p v ~ q C) ~ (p  p)  p  ~ q D) ~ (p  q)  ~ p  ~ q.4) The contrapositive of (p v q)  r is A) r  (p v q) B) ~ r  (p v q) C) ~ r  ~ p ~ q D) P  (q v r).5) For the circuit shown below, the Boolean polynomial is A) (~ p v q) ( p v ~q) B) (~ p  p)  (~ q  q) C) (~p  ~q)  (q  p) D) (~p  q)  (p  ~q).
2. 2. 6) Let p be the proposition : Mathematics is interesting and let q be the proposition that mathematics is difficult, the symbol p  q means A) Mathematics is interesting Implies that mathematics is difficult B) mathematics is interesting implies and is implied by mathematics is difficult C) Mathematics is interesting and mathematics is difficult D) Mathematics is interesting or mathematics is difficult7) The false statement in the following is A) p  (~ p) is a contradiction B) (p q)  (~ q~ p) is a contradiction C) ~ (~ p)  p is a tautology D) p v (~ p) is a tautology8) If p  (~ p v q) is false, the truth values of p and q are respectively A) F, T B) F, F C) T, T D) T, F9) Which of the following is the inverse of the proposition “If a number is prime, then it is odd”? A) it is a number is not a prime, then it is odd B) if is a number is not a prime, then it is odd C) if is a number is not a odd, then it is a prime D) if is a number is odd, then it is a prime10 ) The contrapositive of “If two triangles are identical, then these are similar” is A) If two triangles are not similar, then these are not identical B) If two triangles are not identical, then these are not similar C) If two triangles are not identical, then these are similar D) If two triangles are not similar, then these are identical11 ) If p (~pvq) is false, the truth value of p & q are respectively A) T, T B) T, F C) F, T D) F, F12 ) The false statement in the following is A) ~ (~p)  p is a tautology. B) p v (~p) is a tautology. C) p^ (~p) is a contradiction.
3. 3. D) (pq)  (~q ~p) is a contradiction.13 ) (p^ ~q) ^ (~p v q) is A) Neither a tautology nor a contradiction B) Both a tautology and a contradiction. C) A contradiction D) A tautology.14 ) Which of the following is not the proposition? A) 5 is an even integer B) Mathematics is interesting C) square root of 2 is irrational D) 3 is a prime.15 ) Which of the following is the inverse of propositions: “If a number is prime then it is odd”? A) If a number is not a prime then it is not odd. B) If a number is not a prime then it is odd. C) If number is odd then it is a prime. D) If a number is not odd then it is not a prime.16 ) The converse of the contrapositive of p  q is A) ~pq B) P~q C) ~p~q D) ~qp17 ) The law a+b=b+a is called A) Closure law B) Associative law C) Commutative law D) Distributive law18) “The diagonals of a rhombus are perpendicular” The contrapositive of the above statement is: A) If the diagonal are not perpendicular then the figure is not a rhombus. B) If the diagonals are not perpendicular then the figure is a rhombus. C) If the diagonals are perpendicular then the figure is a rhombus. D) If the figure is not a rhombus, then it’s diagonals are not perpendicular.19) The negation of the proposition ‘if a quadrilateral is a square, then it is a rhombus.’ A) if a quadrilateral is not a square, then it is a rhombus
4. 4. B) if a quadrilateral is a square, then it is not a rhombus C) a quadrilateral is a square and it is not a rhombus D) a quadrilateral is not a square and it is a rhombus20) p  q  p is A) a tautology B) a contradiction C) neither tautology nor contradiction D) none of these21) If p  (q  r) is false, then the truth values of p, q, r are respectively…. A) T, T, T B) F, T, T C) F, F, F D) T, F, F22) The logical equivalent of p  q is A) p  ~q B) ~p  ~q) C) ~ (p  ~q) D) ~ (~p  ~q)23) Which of the following is contradiction? A) (p  q)  ~ (p  q) B) p  (~p  q) C) (p  q)  p D) None of these24) Which of the following is a proposition? A) I am a lion B) an half open door is half closed C) a triangle is a circle and 10 is a prime number D) Logic is an interesting subject.25) Which of the following is wrong? A) p  q is logically equivalent to ~ p  q B) if the truth values of p,q, r are T, F, T respectively then the truth values of C) (p  q)  (q  r) is T. D) ~ (p  q  r)  ~ p  ~ q  ~ r. E) The truth value of p  ~ (p  q) is always T.26) Which of the following is true for the proposition p and q? A) p  q is true when at least one of p and q is true B) p  q is true when p is true and q is false
5. 5. C) p  q is true when both p and q are true D) ~ (p  q) is true only when both p and q are false27) Let there be two propositions: P: I take only bread and breakfast q: I don’t take anything for breakfast Then the compound proposition. “ I take only bread for breakfast or I don’t take anything” is represented as’ A) pq B) pq C) pq D) pq28) Let p and q denotes the following propositions: P: A quadrilateral is a parallelogram Q: The opposite sides are parallel Then the compound proposition: “A quadrilateral is a parallelogram if and only if The opposite are parallel”, is represent by A) pq B) pq C) pq D) pq29) Let p and q be the propositions: p:  ABC is a right angled triangle q: The Pythagoras theorem is obeyed Then, q  p is the compound statement A) The phythagoras theorem is obeyed if and only if the  ABC is a right angled triangle B) The phythagoras theorem is obeyed if  ABC is a right angled triangle C)  ABC is a right angled triangle and the pythagoras theorem is obeyed D) Pythagoras theorem is obeyed or  ABC is a right angled triangle30) Let p and q denote, p: I take medicine, q:I can sleep. Then the compound statement ~ p  ~ q means (a) If I don’t take medicine I cannot sleep A) (b) If I don’t take medicine I can sleep B) (c) I take medicine if and only if I can sleep C) I take medicine if I can sleep31) The logically equivalent proposition of p  q is A) (p  q)  (q  p) B) (p  q)  (q  p) C) (p  q)  (p  q) D) (p  q)  (p  q)
6. 6. 32) Negation of the statement p  (q  r) is …….. A) ~ p  ~ (q  r) B) ~ p  ~ (q  r) C) (p  q)  p D) p  (~ q  ~ r)33) Negation of the statement (p  r)  (r  q) is A) (p  r)  (~ r  ~ q) B) ~ (p  r)  ~ (r  q) C) ~ ( p  r)  ~ (r  q) D) (p  r)  (r  -q)34) ~ p  ~ q is logically equivalent to A) ~ p~ q B) pq C) p~ q D) None of these35) p  (q  r) is logically equivalent to A) p  (q  r) B) (p  q)  r C) (pq)  r D) p  (q  r)36) Let there be two propositions p: It is raining q: It is pleasant Then the compound proposition, “It is neither raining nor pleasant” is representedas A) ~ p~ q B) ~ p~ q C) ~ pq D) ~ pq37) p: It is raining, q: It is pleasant Then the compound proposition, “It is not raining still it is pleasant” is represented as A) ~ pq B) ~ pq C) ~ pq D) None of these
7. 7. 38) Take p for hard work, q for success, and r for job then (p  q)  ~r is the compound statement. A) He worked hard and was successful in exam but could not get a job B) It is not true that he worked hard or was successful and got a job C) He worked hard and was successful and got a job D) None of these39) The negation of the statement “Ashutosh is honest and he is rich” is A) Ashutosh is neither honest nor rich B) Ashutosh is not honest or he is not rich C) it is false that Ashutosh is not honest and he is not rich D) None of these40) The negation of the statement “10>5 and 2<7” is…… A) 10< 5 or 2> 7 B) 10< 5 and 2> 7 C) 10<5 or 2<7 D) None41) The logical statement (pq )  (~p  ~q) is A) a tautology B) a contradiction C) a contingency D) None of these42) The logical statement ~ (p  q ) is equivalent to A) p  ~q B) ~q  ~p C) ~p  ~q D) ~p  q.43) The contra positive of the logical statement p  q is ………….. A) qp B) ~p  ~q C) ~q  ~p D) ~p  q44) p: The cheap food is not good food q: Good food is not cheap food The statement r and q are A) Logically equivalent B) Not logically equivalent C) One is the negation of the other D) None of these
8. 8. 45) Let there be two propositions: p: Mumbai is in Maharashtra q: Madras is in Tamilnadu. Then the compound proposition, Mumbai is in Maharashtra and Madras is in Tamilnadu is represented as: A) pq B) pq C) ~p  q D) ~q  ~p46) Write the following compound statement symbolically: Hari is intelligent or he is hard working. A) pq B) p  ~q C) pq D) ~p  q47) Write the following compound statement symbolically: If it rains the atmospheric humidity increases. A) pq B) pq C) (c) p  q D) pq48) Write the following compound statement symbolically: The school is open or there is a holiday A) pq B) pq C) p  ~q D) ~p  q49) Write the following compound statement symbolically: If it rains heavily then the school will be closed. A) pq B) p  -q C) ~p  ~q D) pq
9. 9. 50) Write the following compound statement symbolically: An angle is right angle if and only if it is of measure 900 A) pq B) p  ~q C) pq D) ~p  q51) Let there be two proposition: p: Prices increases q: Demand falls The compound proposition, ‘If price increases then demand falls’. is represented as A) pq B) p  ~q C) pq D) pq52) Let there be two propositions: p: Seema is fat q:Seema is happy The compound proposition, ‘If seema is fat then she is happy’ represented as, A) pq B) pq C) pq D) pq53) Write the following compound statement symbolically: If it is cloudy then it does not rain A) q  ~p B) pq C) pq D) pq54) Write the following compound statement symbolically: If it is not cloudy then it does not rain A) pq B) ~q  ~p C) p  ~q D) pq55) Write the following compound statement symbolically: the sun has set but the moon has not risen A) pq B) pq
10. 10. C) ~p  q D) p  ~q56) Let there be two propositions: p: The drug is effective q: Drugs has side effects The compound proposition ‘The drug is effective and has side effects is represents as A) pq B) pq C) pq D) pq57) Write the following compound statement symbolically: Either Sachin hits century or Vinod hits century. A) pq B) p  ~q C) pq D) pq58) Let there be two propositions: p: Monotinoc sequence is bounded q: It is convergent The compound proposition is ‘A monotonic sequence is bounded if and only if it is convergent. A) pq B) pq C) p  ~q D) pq59) Let there be two propositions: P: He is intelligent Q: He is studious The compound proposition of ‘Either he is intelligent or he is studious’. A) q  ~p B) pq C) pq D) pq
11. 11. 60) Suppose p is first part and q is second part of following statement. Convert it into symbolic form. p:The sky is blue q: the rose is red The compound proposition is ‘The sky is blue and the rose id red, represents as A) pq B) pq C) p  ~q D) pq61) Let there be two propositions: p: The number is even q: It is divisible the compound proposition is ‘A number is even if and only if it is divisible by 2’ which is represent as A) pq B) pq C) p  ~q D) pq62) Suppose p is first part and q is second part of following statement. Convert it into symbolic form: p: The proof is lengthy q; It is interesting The compound proposition is ‘The proof is lengthy but it is interesting, represents as A) pq B) pq C) pq D) none of these
12. 12. BOOLEAN 20 A 42 AALGEBRA 21 D 43 C OPTIONS 22 C 44 ASR. NO. ANS 23 A 45 A 1 B 24 D 46 C 2 C 25 D 47 B 3 C 26 D 48 B 4 C 27 B 49 D 5 D 28 D 50 A 6 C 29 A 51 D 7 B 30 A 52 C 8 D 31 A 53 A 9 B 32 D 54 B 10 A 33 A 55 D 11 B 34 B 56 A 12 D 35 B 57 C 13 C 36 B 58 D 14 B 37 A 59 B 15 D 38 A 60 A 16 C 39 B 61 D 17 C 40 A 62 C 18 A 41 B 19 C