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question_answer1)
Which of the following is a statement
A)
Open the door done
clear
B)
Do your homework done
clear
C)
Switch on the fan done
clear
D)
Two plus two is four done
clear
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question_answer2)
Which of the following is a statement
A)
May you live long ! done
clear
B)
May God bless you ! done
clear
C)
The sun is a star done
clear
D)
Hurrah ! we have won the match done
clear
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question_answer3)
Which of the following is not a statement
A)
Roses are red done
clear
B)
New Delhi is in India done
clear
C)
Every square is a rectangle done
clear
D)
Alas ! I have failed done
clear
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question_answer4)
Which of the following is not a statement
A)
Every set is a finite set done
clear
B)
8 is less than 6 done
clear
C)
Where are you going? done
clear
D)
The sum of interior angles of a triangle is 180 degrees done
clear
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question_answer5)
Which of the following is not a statement
A)
Please do me a favour done
clear
B)
2 is an even integer done
clear
C)
2 + 1 = 3 done
clear
D)
The number 17 is prime done
clear
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question_answer6)
Which of the following is not a statement
A)
Give me a glass of water done
clear
B)
Asia is a continent done
clear
C)
The earth revolved round the sun done
clear
D)
The number 6 has two prime factors 2, 3 done
clear
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question_answer7)
Which of the following is an open statement
A)
x is a natural number done
clear
B)
Give me a glass of water done
clear
C)
Wish you best of luck done
clear
D)
Good morning to all done
clear
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question_answer8)
Negation of the conditional : ?If it rains, I shall go to school? is
A)
It rains and I shall go to school done
clear
B)
It rains and I shall not go to school done
clear
C)
It does not rains and I shall go to school done
clear
D)
None of these done
clear
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question_answer9)
Negation of ?Paris in France and London is in England? is
A)
Paris is in England and London is in France done
clear
B)
Paris is not in France or London is not in England done
clear
C)
Paris is in England or London is in France done
clear
D)
None of these done
clear
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question_answer10)
Negation is ?2 + 3 = 5 and 8 < 10? is
A)
2 + 3 ¹ 5 and < 10 done
clear
B)
2 + 3 = 5 and 8 ≮ 10 done
clear
C)
2 + 3 ¹ 5 or 8 ≮ 10 done
clear
D)
None of these done
clear
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question_answer11)
Negation of ?Ram is in Class X or Rashmi is in Class XII? is
A)
Ram is not in class X but Ram is in class XII done
clear
B)
Ram is not in class X but Rashmi is not in class XII done
clear
C)
Either Ram is not in class X or Ram is not in class XII done
clear
D)
None of these done
clear
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question_answer12)
The conditional \[(p\wedge q)\] Þ p is
A)
A tautology done
clear
B)
A fallacy i.e., contradiction done
clear
C)
Neither tautology nor fallacy done
clear
D)
None of these done
clear
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question_answer13)
Which of the following is a contradiction
A)
\[(p\wedge q)\wedge \tilde{\ }(p\vee q)\] done
clear
B)
\[p\vee (\tilde{\ }p\wedge q)\] done
clear
C)
\[(p\Rightarrow q)\Rightarrow p\] done
clear
D)
None of these done
clear
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question_answer14)
Which of the following is logically equivalent to \[\tilde{\ }(\tilde{\ }p\Rightarrow q)\]
A)
\[p\wedge q\] done
clear
B)
\[p\wedge \tilde{\ }q\] done
clear
C)
\[\tilde{\ }p\wedge q\] done
clear
D)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
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question_answer15)
\[\tilde{\ }(p\vee q)\] is equal to
A)
\[\tilde{\ }p\ \vee \tilde{\ }q\] done
clear
B)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
C)
\[\tilde{\ }p\vee q\] done
clear
D)
\[p\ \vee \tilde{\ }q\] done
clear
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question_answer16)
\[\tilde{\ }(p\wedge q)\] is equal to
A)
\[\tilde{\ }p\ \vee \tilde{\ }q\] done
clear
B)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
C)
\[\tilde{\ }p\wedge q\] done
clear
D)
\[p\ \wedge \tilde{\ }q\] done
clear
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question_answer17)
\[(\tilde{\ }(\tilde{\ }p))\wedge q\] is equal to
A)
\[\tilde{\ }p\wedge q\] done
clear
B)
\[p\wedge q\] done
clear
C)
\[p\ \wedge \tilde{\ }q\] done
clear
D)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
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question_answer18)
\[\tilde{\ }(p\vee (\tilde{\ }q))\] is equal to
A)
\[\tilde{\ }p\vee q\] done
clear
B)
\[(\tilde{\ }p)\wedge q\] done
clear
C)
\[\tilde{\ }p\ \vee \tilde{\ }p\] done
clear
D)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
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question_answer19)
\[\tilde{\ }((\tilde{\ }p)\ \wedge q)\] is equal to
A)
\[p\vee (\tilde{\ }q)\] done
clear
B)
\[p\vee q\] done
clear
C)
\[p\wedge (\tilde{\ }q)\] done
clear
D)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
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question_answer20)
\[\tilde{\ }(p\Leftrightarrow q)\] is
A)
\[\tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
B)
\[\tilde{\ }p\ \vee \tilde{\ }q\] done
clear
C)
\[(p\ \wedge \tilde{\ }q)\vee (\tilde{\ }p\ \wedge q)\] done
clear
D)
None of these done
clear
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question_answer21)
\[p\Rightarrow q\] can also be written as
A)
\[p\Rightarrow \ \tilde{\ }q\] done
clear
B)
\[\tilde{\ }p\vee q\] done
clear
C)
\[\tilde{\ }q\Rightarrow \tilde{\ }p\] done
clear
D)
None of these done
clear
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question_answer22)
If p, q, r are simple propositions with truth values T, F, T, then the truth value of \[(\tilde{\ }p\vee q)\ \wedge \tilde{\ }r\Rightarrow p\] is
A)
True done
clear
B)
False done
clear
C)
True if r is false done
clear
D)
True if q is true done
clear
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question_answer23)
If \[(p\ \wedge \tilde{\ }r)\Rightarrow (q\vee r)\] is false and q and r are both false, then p is
A)
True done
clear
B)
False done
clear
C)
May be true or false done
clear
D)
Data insufficient done
clear
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question_answer24)
If p, q, r are simple propositions, then \[(p\wedge q)\wedge (q\wedge r)\] is true then
A)
p, q, r are all false done
clear
B)
p, q, r are all true done
clear
C)
p, q are true and r is false done
clear
D)
p is true and q and r are false done
clear
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question_answer25)
\[\tilde{\ }(p\Rightarrow q)\Leftrightarrow \tilde{\ }p\ \vee \tilde{\ }q\] is
A)
A tautology done
clear
B)
A contradiction done
clear
C)
Neither a tautology nor a contradiction done
clear
D)
Cannot come to any conclusion done
clear
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question_answer26)
\[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\vee q)\] is
A)
A contradiction done
clear
B)
A tautology done
clear
C)
Either A or B done
clear
D)
Neither A nor B done
clear
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question_answer27)
Which of the following is not logically equivalent to the proposition : ?A real number is either rational or irrational?.
A)
If a number is neither rational nor irrational then it is not real done
clear
B)
If a number is not a rational or not an irrational, then it is not real done
clear
C)
If a number is not real, then it is neither rational nor irrational done
clear
D)
If a number is real, then it is rational or irrational done
clear
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question_answer28)
If p : It rains today, q : I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
A)
\[\tilde{\ }(p\wedge q)\Rightarrow (r\wedge s)\] done
clear
B)
\[\tilde{\ }(p\ \wedge \tilde{\ }q)\Rightarrow (r\wedge s)\] done
clear
C)
\[\tilde{\ }(p\ \wedge q)\ \Rightarrow (r\vee s)\] done
clear
D)
None of these done
clear
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question_answer29)
The negation of the compound proposition \[p\vee (\tilde{\ }p\vee q)\] is
A)
\[(p\ \wedge \tilde{\ }q)\ \wedge \tilde{\ }p\] done
clear
B)
\[(p\ \wedge \tilde{\ }q)\ \vee \tilde{\ }p\] done
clear
C)
\[(p\ \vee \tilde{\ }q)\ \vee \tilde{\ }p\] done
clear
D)
None of these done
clear
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question_answer30)
Which of the following is true
A)
\[p\Rightarrow q\equiv \ \tilde{\ }p\Rightarrow \ \tilde{\ }q\] done
clear
B)
\[\tilde{\ }(p\Rightarrow \ \tilde{\ }q)\equiv \ \tilde{\ }p\wedge q\] done
clear
C)
\[\tilde{\ }(\tilde{\ }p\Rightarrow \,\tilde{\ }q)\equiv \tilde{\ }p\wedge q\] done
clear
D)
\[\tilde{\ }(p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)]\] done
clear
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question_answer31)
\[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\] is logically equivalent to
A)
~p done
clear
B)
p done
clear
C)
q done
clear
D)
~q done
clear
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question_answer32)
The inverse of the proposition \[(p\ \wedge \tilde{\ }q)\Rightarrow r\] is
A)
\[\tilde{\ }r\Rightarrow \ \tilde{\ }p\vee q\] done
clear
B)
\[\tilde{\ }p\vee q\Rightarrow \ \tilde{\ }r\] done
clear
C)
\[r\Rightarrow p\ \wedge \tilde{\ }q\] done
clear
D)
None of these done
clear
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question_answer33)
When does the current flow through the following circuit
A)
p, q, r should be closed done
clear
B)
p, q, r should be open done
clear
C)
Always done
clear
D)
None of these done
clear
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question_answer34)
Which Venn diagram represent the truth of the statement ?All students are hard working.? Where U = Universal set of human beings S = Set of all students H = Set of all hard workers
A)
B)
C)
D)
None of these done
clear
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question_answer35)
Which Venn diagram represent the truth of the statements ?No child is naughty? Where U = Universal set of human beings C = Set of children N = Set of naughty persons
A)
B)
C)
D)
None of these done
clear
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question_answer36)
Which Venn diagram represent the truth of the statement ?No policeman is a thief?
A)
B)
C)
D)
None of these done
clear
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question_answer37)
Which Venn diagram represent the truth of the statement ?Some teenagers are not dreamers?
A)
B)
C)
D)
None of these done
clear
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question_answer38)
Which of the following Venn diagram corresponds to the statement ?All mothers are women? (M is the set of all mothers, W is the set of all women)
A)
B)
C)
D)
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question_answer39)
The negative of \[q\ \vee \tilde{\ }(p\wedge r)\] is [Karnataka CET 1997]
A)
\[\tilde{\ }q\ \wedge \tilde{\ }(p\wedge r)\] done
clear
B)
\[\tilde{\ }q\wedge (p\wedge r)\] done
clear
C)
\[\tilde{\ }q\vee (p\wedge r)\] done
clear
D)
None of these done
clear
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question_answer40)
The propositions \[(p\Rightarrow \ \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a [Karnataka CET 1997]
A)
Tautology and contradiction done
clear
B)
Neither tautology nor contradiction done
clear
C)
Contradiction done
clear
D)
Tautology done
clear
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question_answer41)
Which of the following is always true [Karnataka CET 1998]
A)
\[(p\Rightarrow q)\equiv \ \tilde{\ }q\Rightarrow \ \tilde{\ }p\] done
clear
B)
\[\tilde{\ }(p\vee q)\equiv \vee \ p\ \vee \tilde{\ }q\] done
clear
C)
\[\tilde{\ }(p\Rightarrow q)\equiv p\ \wedge \tilde{\ }q\] done
clear
D)
\[\tilde{\ }(p\vee q)\equiv \ \tilde{\ }p\ \ \wedge \tilde{\ }q\] done
clear
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question_answer42)
The contrapositive of \[(p\vee q)\Rightarrow r\] is [Karnataka CET 1999]
A)
\[r\Rightarrow (p\vee q)\] done
clear
B)
\[\tilde{\ }r\Rightarrow (p\vee q)\] done
clear
C)
\[\tilde{\ }r\Rightarrow \ \tilde{\ }p\ \wedge \tilde{\ }q\] done
clear
D)
\[p\Rightarrow (q\vee r)\] done
clear
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question_answer43)
If \[p\Rightarrow (q\vee r)\] is false, then the truth values of p, q, r are respectively [Karnataka CET 2000]
A)
T, F, F done
clear
B)
F, F, F done
clear
C)
F, T, T done
clear
D)
T, T, F done
clear
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question_answer44)
The logically equivalent proposition of \[p\Leftrightarrow q\] is [Karnataka CET 2000]
A)
\[(p\wedge q)\vee (p\wedge q)\] done
clear
B)
\[(p\Rightarrow q)\wedge (q\Rightarrow p)\] done
clear
C)
\[(p\wedge q)\vee (q\Rightarrow p)\] done
clear
D)
\[(p\wedge q)\Rightarrow (q\vee p)\] done
clear
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question_answer45)
The false statement in the following is [Karnataka CET 2002]
A)
\[p\wedge (\tilde{\ }p)\] is a contradiction done
clear
B)
\[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \ \tilde{\ }p)\] is a contradiction done
clear
C)
\[\tilde{\ }(\tilde{\ }p)\Leftrightarrow p\] is a tautology done
clear
D)
\[p\vee (\tilde{\ }p)\]Û is a tautology done
clear
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question_answer46)
If \[p\Rightarrow (\tilde{\ }p\vee q)\] is false, the truth values of p and q are respectively [Karnataka CET 2002]
A)
F, T done
clear
B)
F, F done
clear
C)
T, T done
clear
D)
T, F done
clear
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question_answer47)
Which of the following is not a proposition [Karnataka CET 2002]
A)
\[\sqrt{3}\] is a prime done
clear
B)
\[\sqrt{2}\] is irrational done
clear
C)
Mathematics is interesting done
clear
D)
5 is an even integer done
clear
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question_answer48)
\[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is [Karnataka CET 2003]
A)
A tautology done
clear
B)
A contradiction done
clear
C)
Both a tautology and a contradiction done
clear
D)
Neither a tautology nor a contradiction done
clear
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question_answer49)
\[\tilde{\ }p\wedge q\] is logically equivalent to [Karnataka CET 2004]
A)
\[p\to q\] done
clear
B)
\[q\to p\] done
clear
C)
\[\tilde{\ }(p\to q)\] done
clear
D)
\[\tilde{\ }(q\to p)\] done
clear
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question_answer50)
Which of the following is the inverse of the proposition: ?If a number is a prime then it is odd.? [Karnataka CET 2004]
A)
If a number is not a prime then it is odd done
clear
B)
If a number is not a prime then it is odd done
clear
C)
If a number is not odd then it is not a prime done
clear
D)
If a number is not odd then it is a prime done
clear
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