11th
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Professional Development

Mathematics, Architecture, Computers

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Shreya Kumbhar

3 years

Mathematics, Architecture, Computers

11th -

Professional Development

Mathematical Logic

Shreya Kumbhar

62
plays

30 questions

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1. Multiple Choice
1 minute
1 pt
$\left(p\wedge q\right)\rightarrow r\$ is logically equivalent to
$p\rightarrow\left(q\rightarrow r\right)$
$\left(p\wedge q\right)\rightarrow\sim r$
$\left(\sim p\vee\sim q\right)\rightarrow\sim r$
$\left(p\vee q\right)\rightarrow r$
2. Multiple Choice
1 minute
1 pt
The negation of $p\wedge\left(q\rightarrow r\right)$ is
$\sim p\wedge\left(\sim q\rightarrow\sim r\right)$
$p\vee\left(\sim q\vee r\right)$
$\sim p\wedge\left(\sim q\rightarrow\sim r\right)$
$\sim p\vee\left(\sim q\wedge\sim r\right)$
3. Multiple Choice
1 minute
1 pt
Examine $\left(p\wedge q\right)\wedge\left(\sim p\vee\sim q\right)$
Tautology
Contradiction
Contingency
None of these
4. Multiple Choice
1 minute
1 pt
Dual of $\left(p\wedge t\right)\vee\left(c\wedge\sim q\right)$
$\left(p\vee c\right)\wedge\left(t\wedge q\right)$
$\left(p\vee c\right)\wedge\left(c\wedge\sim q\right)$
$\left(p\wedge c\right)\vee\left(t\wedge q\right)$
$\left(p\vee c\right)\wedge\left(t\vee\sim q\right)$
5. Multiple Choice
1 minute
1 pt
7>3 and 4 >11 Negation of Statement is
$7<3\ or\ 4<11$
$7\le3\ and\ 4\le11$
$7\le3\ or\ 4\le11$
$7\ne3\ and\ 4\ne11$
6. Multiple Choice
1 minute
1 pt
"If a Function is differentiable then it is Continuous."What is Contra-positive of Statement .
If a function is not continuous then it is not differentiable
If a function is not differentiable then it is not continuous.
If a function is continuous then it is differentiable
If a function is not continuous then it is differentiable.
7. Multiple Choice
1 minute
1 pt
Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.
If I do not have a Siberian Husky, then I do not have a dog.
If I have a dog, then I have a Siberian Husky.
If I do not have a dog, then I do not have a Siberian Husky.
If I do not have a Siberian Husky, then I have a dog.
8. Multiple Choice
1 minute
1 pt
If $p$ and $q$ are two statements, then statement $p\longrightarrow q\ \wedge\sim q$ is
Tautology
Contradiction
Neither Tautology nor contradiction
None of the above
9. Multiple Choice
1 minute
1 pt
Let $p\wedge\left(q\vee r\right)=\left(p\wedge q\right)\vee\left(p\wedge r\right)$ .
Then, this law is known as.......
Commutative Law
Associative law
De-Morgan's Law
Distributive Law
10. Multiple Choice
1 minute
1 pt
Truth value of the statement "if p then q" is false when
p is true, q is true
p is true, q is false
p is false, q is true
p is false, q is false
11. Multiple Choice
1 minute
1 pt
Which of the following is the statement?
May you live long !
May God bless you !
The Sun is star
Hurrah ! We have won the match
12. Multiple Choice
1 minute
1 pt
Which of the following is not the statement?
Where are you going?
8 is less than 6
The sum of interior angles of a triangles is 180 degrees
Every set is a finite set
13. Multiple Choice
1 minute
1 pt
For any two statements p and q, the negation of the expression $p\vee\left(\sim p\wedge q\right)$ is
$\sim p\ \vee\sim q$
$\sim p\ \wedge\sim q$
$p\wedge q$
$p\longleftrightarrow q$
14. Multiple Choice
1 minute
1 pt
Negation of "Ram is in Class X or Rashmi is in Class XII" is
Ram is not in class X but Ram is in class XII
Ram is not in class X but Rashmi is not in class XII
Either Ram is not in class X or Ram is not in class XII
None of these
15. Multiple Choice
1 minute
1 pt
Which of the following is logically equivalent to $\sim(p\longleftrightarrow q)$
$\sim p∧\sim\ q$
$\sim p∨\sim q$
$(p∧\sim q)∨(\sim p∧q)$
None of these
16. Multiple Choice
1 minute
1 pt
If
p : It rains today
q : I go to school
r : I shall meet any friends
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.
$\sim(p∧q)\longrightarrow(r∧s)$
$\sim(p∧\sim q)\longrightarrow(r∧s)$
$\sim(p∧q)\longrightarrow(r∨s)$
None of these
17. Multiple Choice
1 minute
1 pt
Which of the following is true
$p\longrightarrow q≡\sim p\longrightarrow\sim q$
$\sim(p\longrightarrow\sim q)≡\sim p∧q$
$\sim(\sim p\longrightarrow\sim q)≡\sim p∧q$
$\sim(p\longleftrightarrow q)≡\sim(p\longrightarrow q)∧\sim(q\longrightarrow p)$
18. Multiple Choice
1 minute
1 pt
If $p\longrightarrow(\sim p∨q)$ is false, the truth values of p and q are respectively
F, T
F, F
T, T
T, F
19. Multiple Choice
1 minute
1 pt
The false statement in the following is
$p∧(\sim p)$ is a contradiction
$(p\longrightarrow q)\longleftrightarrow(\sim q\longrightarrow\sim p)$ is a contradiction
$(\sim p)\longleftrightarrow p$ is a tautology
$p∨(\sim p)$ is a tautology
20. Multiple Choice
1 minute
1 pt
If $p\longrightarrow(q∨r)$ is false, then the truth values of p, q, r are respectively
T, F, F
F, F, F
F, T, T
T, T, F
21. Multiple Choice
1 minute
1 pt
Which of the following is not logically equivalent to the proposition : A real number is either rational or irrational.
If a number is neither rational nor irrational then it is not real
If a number is not a rational or not an irrational, then it is not real
If a number is not real, then it is neither rational nor irrational
If a number is real, then it is rational or irrational
22. Multiple Choice
1 minute
1 pt
If p, q, r are simple propositions, then $(p∧q)∧(q∧r)$ is true then
p, q, r are all false
p is true and q and r are false
p, q are true and r is false
p, q, r are all true
23. Multiple Choice
1 minute
1 pt
If $(p∧\sim r)\longrightarrow(q∨r)$ is false and q and r are both false, then p is
True
False
May be true or false
Data insufficient
24. Multiple Choice
1 minute
1 pt
If p, q, r are simple propositions with truth values T, F, T, then the truth value of $(\sim p∨q)∧\sim r\longrightarrow p$ is
True if q is true
False
True if r is false
True
25. Multiple Choice
1 minute
1 pt
$p\longrightarrow q$
can also be written as
$p\longrightarrow\sim q$
$\sim p∨q$
$\sim q\longrightarrow\sim p$
None of these
26. Multiple Choice
1 minute
1 pt
p: Ram is coward
q: ram is lazy
r: ram is rich
Identify statement for "It is not true that ram is not rich"
$\sim p\vee\sim q$
$\sim p\vee\sim r$
$\sim(\sim r)$
$\sim(\sim q)$
27. Multiple Choice
1 minute
1 pt
Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?
If a polygon is not a quadrilateral, then it is not a trapezoid.
If a polygon is not a trapezoid, then it is not a quadrilateral.
If a polygon is a trapezoid, then it is a quadrilateral.
A rectangle is also a quadrilateral.
28. Multiple Choice
1 minute
1 pt
Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?
If a polygon is a trapezoid, then it is a quadrilateral.
If a polygon is not a quadrilateral, then it is not a trapezoid.
If a polygon is not a trapezoid, then it is not a quadrilateral.
A rectangle is also a quadrilateral.
29. Multiple Choice
1 minute
1 pt
If a represents "Brent works this summer" and b represents "Brent takes a vacation" which symbols best represent the statement "If Brent works this summer then he will not take a vacation."
a → b
b→ a
a → ~ b
~a → ~ b
30. Multiple Choice
1 minute
1 pt
Given-

p is TRUE
q is FALSE

Which of the following statements is FALSE?
$p\wedge\sim q$
$\sim\left(q\right)$
$p\rightarrow q$
$p\vee q$
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Mathematical Logic

11th - Professional Development

Mathematics, Architecture, Computers

Mathematics, Architecture, Computers

11th -

Professional Development

Mathematical Logic

62 plays

30 questions

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11th
-
Professional Development

62
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