1. Which of the following statement is a proposition?
a) Get me a glass of milkshake
b) God bless you!
c) What is the time now?
d) The only odd prime number is 2
Answer: d
Explanation: Only this statement has got the truth value which is false.
2. The truth value of ‘4+3=7 or 5 is not prime’.
a) False
b) True
Answer: b
Explanation: Compound statement with ‘or’ is true when either of the statement is true. Here the first part of the statement is true, hence the whole is true.
3. Which of the following option is true?
a) If the Sun is a planet, elephants will fly
b) 3 +2 = 8 if 5-2 = 7
c) 1 > 3 and 3 is a positive integer
d) -2 > 3 or 3 is a negative integer
Answer: a
Explanation: Hypothesis is false, thus the whole statement is true.
4. What is the value of x after this statement, assuming the initial value of x is 5? ‘If x equals to one then x=x+2 else x=0’.
a) 1
b) 3
c) 0
d) 2
Answer: c
Explanation: If condition is false so value decided according to else condition.
5. Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is?
a) If I love cricket then I am in Bangalore
b) If I am in Bangalore then I love cricket
c) I am not in Bangalore
d) I love cricket
Answer: a
Explanation: Q is hypothesis and P is conclusion. So the compound statement will be if hypothesis then conclusion.
6. Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true?
a) Raju bowled and Sahil got out on first ball
b) Raju did not bowled
c) Sahil bowled and Saurabh hits a century
d) Sahil bowled and Saurabh got out
Answer: c
Explanation: Either hypothesis should be false or both (hypothesis and conclusion) should be true.
7. The truth value ‘9 is prime then 3 is even’.
a) False
b) TTru
Answer: b
Explanation: The first part of the statement is false, hence whole is true.
Let P: I am in Delhi.; Q: Delhi is clean.; then q ^ p(q and p) is?
a) Delhi is clean and I am in Delhi
b) Delhi is not clean or I am in Delhi
c) I am in Delhi and Delhi is not clean
d) Delhi is clean but I am in Mumbai
Answer: a
Explanation: Connector should be ‘and’, that is q and p.
Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ Is best represented by?
a) ~P V ~Q
b) P ∧ ~Q
c) P V Q
d) P ∧ Q
Answer: b
Explanation: The second part of the statement is negated, hence negation operator is used.
10. Let P: We should be honest., Q: We should be dedicated., R: We should be overconfident. Then ‘We should be honest or dedicated but not overconfident.’ Is best represented by?
a) ~P V ~Q V R
b) P ∧ ~Q ∧ R
c) P V Q ∧ R
d) P V Q ∧ ~R
Answer: d
Explanation: The third part of the statement is negated, hence negation operator is used, for (‘or’ –V) is used and for(’but’- ∧).
Which of the following bits is the negation of the bits “010110”?
a) 111001
b) 001001
c) 101001
d) 111111
Answer: c
Explanation: Flip each of the bit to get the negation of the required string.
Which of the following option is suitable, if A is “10110110”, B is”11100000” and C is”10100000”? a) C=A or B
b) C=~A
c) C=~B
d) C=A and B
Answer: c
Explanation: Flip each of the bit to get the negation of the required string.
How many bits string of length 4 are possible such that they contain 2 ones and 2 zeroes? a) 4
b) 2
c) 5
d) 6
Answer: d
Explanation: The strings are {0011, 0110, 1001, 1100, 1010 and 0101}.
If a bit string contains {0, 1} only, having length 5 has no more than 2 ones in it. Then how many such bit strings are possible?
a) 14
b) 12
c) 15
d) 16
Answer: d
Explanation: The total strings are 1(having no one in it) +5(having 1 one in it) +10 (having 2 ones in it) = 16.
If A is “001100” and B is “010101” then what is the value of A (Ex-or) B?
a) 000000
b) 111111
c) 001101
d) 011001
Answer: d
Explanation: In Ex-or if both the inputs are same then output is 0 otherwise 1.
The Ex-nor of this string “01010101” with “11111111” is?
a) 10101010
b) 00110100
c) 01010101
d) 10101001
Answer: c
Explanation: In Ex-nor if both the inputs are same then output is 1 otherwise 0.
. What is the one’s complement of this string “01010100”?
a) 10101010
b) 00110101
c) 10101011
d) 10101001
Answer: c
Explanation: Negate every bit in one’s complement.
What is the negation of the statement A->(B v(or) C)?
a) A ∧ ~B ∧ ~C
b) A->B->C
c) ~A ∧ B v C
d) None of the mentioned
The compound statement A-> (A->B) is false, then the truth values of A, B are respectively _________ a) T, T
b) F, T
c) T, F
d) F, F
Answer: c
Explanation: For implications to be false hypothesis should be true and conclusion should be false.
The statement which is logically equivalent to A∧ (and) B is?
a) A->B
b) ~A ∧ ~ B
c) A ∧ ~B
d) ~(A->~B)
Answer: d
Explanation: The truth table of both statements are same.
Let P: We give a nice overall squad performance, Q: We will win the match.
Then the symbolic form of “We will win the match if and only if we give a nice overall squad performance.“ is?
a) P v Q
b) Q ∧ P
c) Q<->P
d) ~P v Q
Answer: c
Explanation: If and only if statements are bi-conditionals.
Let P, Q, R be true, false true, respectively, which of the following is true?
a) P∧Q∧R
b) P∧~Q∧~R
c) Q->(P∧R)
d) P->(Q∧R)
Answer: c
Explanation: Hypothesis is false, hence statement is true.
“Match will be played only if it is not a humid day.” The negation of this statement is?
a) Match will be played but it is a humid day
b) Match will be played or it is a humid day
c) All of the mentioned statement are correct
d) None of the mentioned
Answer: a
Explanation: Negation of P->Q is P∧~Q.
Consider the following statements.
A: Raju should exercise.
B: Raju is not a decent table tennis player.
C: Raju wants to play good table tennis.
The symbolic form of “Raju is not a decent table tennis player and if he wants to play good table tennis then he should exercise.” Is?
a) A->B->C
b) B∧(C->A)
c) C->B∧A
d) B<->A∧C
Answer: b
Explanation: For conditionals statement (if then), implications are used.
The statement (~P<->Q)∧~Q is true when?
a) P: True Q: False
b) P: True Q: True
c) P: False Q: True
d) P: False Q: False
Answer: a
Explanation: For a bi-conditional to be true both inputs should be same.
Let P, Q, R be true, false, false, respectively, which of the following is true?
a) P∧(Q∧~R)
b) (P->Q)∧~R
c) Q<->(P∧R)
d) P<->(QvR)
Answer: c
Explanation: For a bi-conditional to be true both inputs should be the same.
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