WorksheetsLOGIC DRILL
Total questions: 148
Worksheet time: 2hrs 33mins
“I shall return”, by Mc Arthur
Proposition
Not a Proposition
Every triangle is a polygon.
Proposition
Not Proposition
x is greater than or equal to -2.
Proposition
Not Proposition
If x + 2 = 4, is x = 2?
Proposition
Not Proposition
Define a polynomial function.
Proposition
Not Proposition
Please close the door.
Proposition
Not Proposition
That is a false statement.
Proposition
Not Proposition
f(x) = 2x - 3 = 7, if f(5)
Proposition
Not Proposition
If the elephant were red, therefore it can hide in a cherry tree
Proposition
Not Proposition
3x - 9 = 21
Proposition
Not Proposition
p: I am a student.
q: I am studying logic.
What is p → q?
p: I am a student.
q: I am studying logic.
What is p ↔ q?
p: I am a student.
q: I am studying logic.
What is ∼ p ↔ ∼ q?
p: I am a student.
q: I am studying logic.
What is p ∧ q?
What is the symbol used for the implication statement?
↔
→
∨
∧
What is the symbol used for the biconditional statement?
↔
→
∨
∧
In a disjunction, even if one of the statements is false, the whole disjunction is still...
False
True
Negated
Both False and True
In a conditional statement, the first part is the antecedent and the second part is the _______
Predicate
Subject
Consequent
hypothesis
What is the formula in finding the number of column of Truth tables?
2n
2n
n2
n
If p is True and q is False, what is p → q
True
False
True or False
Can't be determined
If p is False and q is false. What is ∼ p ∨ q
True
False
True or False
Can't be determined
If p is True and q is false. What is ∼ p ↔ ∼ q
True
False
True or False
Can't be determined
If p is True and q is false. What is ∼ p → ∼ q
True
False
True or False
Can't be determined
If p is True and q is True. What is ∼ p ∨ ∼ q
True
False
True or False
Can't be determined
If p is False and q is True. What is ∼ p → ∼ q
True
False
True or False
Can't be determined
(p∧q)→r is logically equivalent to
p→(q→r)
(p∧q)→∼r
(∼p∨∼q)→∼r
(p∨q)→r
The negation of p∧(q→r) is
∼p∧(∼q→∼r)
p∨(∼q∨r)
∼p∧(∼q→∼r)
∼p∨(∼q∧∼r)
Examine (p∧q)∧(∼p∨∼q)
Tautology
Contradiction
Contingency
None of these
Dual of (p∧t)∨(c∧∼q)
(p∨c)∧(t∧q)
(p∨c)∧(c∧∼q)
(p∧c)∨(t∧q)
(p∨c)∧(t∨∼q)
7>3 and 4 >11 Negation of Statement is
7<3 or 4<11
7≤3 and 4≤11
7≤3 or 4≤11
7=3 and 4=11
"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.
If p and q are two statements, then statement p⟶q ∧∼q is
Tautology
Contradiction
Neither Tautology nor contradiction
None of the above
Let p∧(q∨r)=(p∧q)∨(p∧r) .
Then, this law is known as.......
Commutative Law
Associative law
De-Morgan's Law
Distributive Law
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
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
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
For any two statements p and q, the negation of the expression p∨(∼p∧q) is
∼p ∨∼q
∼p ∧∼q
p∧q
p⟷q
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
Which of the following is logically equivalent to ∼(p⟷q)
∼p∧∼ q
∼p∨∼q
(p∧∼q)∨(∼p∧q)
None of these
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.
∼(p∧q)⟶(r∧s)
∼(p∧∼q)⟶(r∧s)
∼(p∧q)⟶(r∨s)
None of these
Which of the following is true
p⟶q≡∼p⟶∼q
∼(p⟶∼q)≡∼p∧q
∼(∼p⟶∼q)≡∼p∧q
∼(p⟷q)≡∼(p⟶q)∧∼(q⟶p)
If p⟶(∼p∨q) is false, the truth values of p and q are respectively
F, T
F, F
T, T
T, F
The false statement in the following is
p∧(∼p) is a contradiction
(p⟶q)⟷(∼q⟶∼p) is a contradiction
(∼p)⟷p is a tautology
p∨(∼p) is a tautology
If p⟶(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
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
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
If (p∧∼r)⟶(q∨r) is false and q and r are both false, then p is
True
False
May be true or false
Data insufficient
If p, q, r are simple propositions with truth values T, F, T, then the truth value of (∼p∨q)∧∼r⟶p is
True if q is true
False
True if r is false
True
p⟶q
can also be written as
p⟶∼q
∼p∨q
∼q⟶∼p
None of these
p: Ram is coward
q: ram is lazy
r: ram is rich
Identify statement for "It is not true that ram is not rich"
∼p∨∼q
∼p∨∼r
∼(∼r)
∼(∼q)
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.
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.
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
Given-
p is TRUE
q is FALSE
Which of the following statements is FALSE?
p∧∼q
∼(q)
p→q
p∨q
An angle is right angle and its measure is 90°
p ⟶ q
p ∨ q
p ∧ q
p ⟷ q
Jupiter is planet and Mars is a star
p ⟶ q
p ∨ q
p ∧ q
p ⟷ q
If the train reaches on time , then I can catch the connecting flight.
p ⟶ q
p ∨ q
p ∧ q
p ⟷ q
If price increases , then demand falls.
p ⟶ q
p ∨ q
p ∧ q
p ⟷ q
ABCD is a parallelogram but it is not a quadrilateral
p ∧ ∼ q
p ⟷ ∼q
p ∨ ∼q
p ⟷ ∼q
Paris is not in France or London is not in England.
∼p ∧∼q
∼p ∨ ∼q
∼ p ⟶ ∼ q
∼ p ⟷ ∼q
If you access the website , then you pay a subscription fee.
p ∧ q
p ∨ q
p ⟶ q
p ⟷ q
It does not rain and I shall go to school.
∼p ⟶ q
∼p ∧ q
∼p ∨ q
∼p ⟷ q
Reshma is tall or she is beautiful
p ∨ q
p ∧ q
p ⟶ q
p ⟷ q
He is rich and happy
p ∧ ∼ q
p ∨ ∼q
p ⟶ ∼q
p ∧ q
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
p: it is cold q: It is raining Find pv~q
It is cold and not raining
It is cold or not raining
It is cold or raining
It is not cold or raining
Which statement has a true truth value?
Fish can walk
Chicken has four legs.
Birds can fly.
Shark has two legs.
"The first even counting number is two," is an example of
An interrogative.
An imperative.
A statement.
An opinion.
Is the following a valid argument:
Every cat chases mice.
Sylvester is a cat.
Therefore, Sylvester chases mice.
No
Yes
Let p represent: The jeep is white.
Let q represent: Molly loves ballet.
Let r represent: He watches netflix.
Which of the following represents the given sentence in symbolic form?
"The jeep is not white."
∼q
∼(∼q)
∼r
∼p
Let p represent: The jeep is white.
Let q represent: Molly loves ballet.
Let r represent: He is watching netflix.
Which of the following represents the given sentence in symbolic form?
"Molly does not love ballet."
q
∼r
∼(∼q)
∼q
Let p represent: The jeep is white.
Let q represent: Molly loves ballet.
Let r represent: He is watching netflix.
Which of the following represents the given sentence in symbolic form?
"It is not the case that he is not watching netflix."
∼r
∼(∼r)
∼q
∼(∼(∼p))
Which of the following goes in the missing boxes? State from top to bottom.
F, F
T, T
F, T
T, F
Let p represent: The jeep is white.
Let q represent: Molly loves ballet.
Let r represent: He watches netflix.
Which of the following represents the given sentence in symbolic form?
"It is not the case that he watches netflix."
∼r
∼p
∼(∼r)
r
Assuming p: She is beautiful, q: She is clever, the verbal form of p ∧ (~q) is
She is beautiful and clever
She is beautiful or not clever.
She is not beautiful and not clever.
She is beautiful but not clever
State whether the following statement is True or False :
Truth value of 2 + 3 < 6 is F.
True
False
A statement written in "if-then" form is a
theorem
conjecture
corollary
conditional statement
Given: p: It is a rainy day today
q: I will watch a movie
r: I will go for a walk
Write the sentence in symbolic form:
"It is a rainy day today and I will not go for a walk."
∼p∨∼r
p∧∼q
p∧∼r
p∨r
Select the term that best describes the statement.
All lines are straight or a triangle has four sides.
negation
conjunction
disjunction
conditional
Select the term that best describes the statement.
If a polygon has eight sides, then it is an octagon.
negation
conjunction
disjunction
conditional
Select the term that best describes the statement.
The lights are on and the TV is off.
negation
conjunction
disjunction
conditional
Select the term that best describes the statement.
A triangle is obtuse provided all the angles have a measure greater than 90 degrees.
negation
conjunction
disjunction
conditional
Select the term that best describes the statement.
Geometry is fun or fish do not like water.
negation
conjunction
disjunction
conditional
Select the term that best describes the statement after the conditional.
Conditional: If two angles add to 90°, then they are complementary.
If two angles are complementary, then they add to 90°.
inverse
converse
contrapositive
Select the term that best describes the statement after the conditional.
Conditional: If two angles add to 90°, then they are complementary.
If two angles are not complementary, then they do not add to 90°.
inverse
converse
contrapositive
Select the term that best describes the statement after the conditional.
Conditional: If two angles add to 90°, then they are complementary.
If two angles do not add to 90°, then they are not complementary.
inverse
converse
contrapositive
Select the term that best describes the statement after the conditional.
Conditional: If it rains, then the flowers bloom.
If the flowers bloom, then it rained.
inverse
converse
contrapositive
Select the term that best describes the statement after the conditional.
Conditional: If it rains, then the flowers bloom.
If the flowers do not bloom, then it did not rain.
inverse
converse
contrapositive
Select the term that best describes the statement after the conditional.
Conditional: If it rains, then the flowers bloom.
If it does not rain, then the flowers will not bloom.
inverse
converse
contrapositive
You eat at several Asian restaurants and decide that Asian food is salty. What type of reasoning is this?
Inductive
Deductive
neither
All professional athletes earn a lot of money. Wes plays professional football so he makes a lot of money. What type of reasoning is this?
Inductive
Deductive
neither
If 60 seconds are in a minute, 60 minutes in an hour, and 24 hours in a day, then 86,400 seconds are in a day. What type of reasoning is this?
Inductive
Deductive
neither
You visit a farm and notice that white chickens lay white eggs and colored chickens lay brown eggs, so you decide that only white chickens lay white eggs. What type of reasoning is this?
Inductive
Deductive
neither
If p is true and q is false, the p --> q is _______
Always true
Sometimes true
Never true
When p is false and q is true, then p or q is _______
Always true
Sometimes true
Never true
When p is false and q is true, then p or q is _______
Always false
Sometimes false
Never false
If p is true and q is true, then ~ p --> ~ q is
Always true
Sometimes true
Never true
If p --> q is true and q is true, then p is
Always true
Sometimes true
Never true
Write the given.
If one angle of a triangle is 90∘, then the other two add to 90∘.
.
Write the to prove statement.
If one angle of a triangle is 90∘, then the other two add to 90∘.
Write the given statement in the following proof.
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Write the to prove statement in the following proof.
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Based on the Table is the Statement in 5 true or false?
t
f
Based on the Table is the Statement in 2 true or false?
T
F
"I do my homework,then I get my allowance."
What is the hypothesis?
I get my allowance.
I do my homework
No answer
All of the above
P : I am young
Q : I am happy
Write “I am old but happy” in symbolic form.
P : I am young
Q : I am happy
Write “I am happy if and only if I am young” in symbolic form.
Choose the correct answer for the following truth table:
T T T F
T F T F
T T T T
T T F F
Which of the following are a variation of a conditional statement?
Conjunction
Converse
Inverse
Contrapostitive
Contranegative
A statement is a(n) (a) if and only if it is always true.
Premise, Conclusion, Contradiction, Tautology, Implication, or Argument.
A statement is a(n) (a) if and only if it is always false.
Premise, Conclusion, Contradiction, Tautology, Implication, or Argument.
Use the following statements:
f. Limes are sour
u. I like sponges
n. The sky is big
What is the symbolic form for the biconditional statement of the first two statements given?
f ⟷ u
f ⟷ n
f ⟶ u
f ⟵ u
How can you put an elephant on the refrigerator?
You can't put it inside
Open the fridge door and put it in
Chop it before putting it in
No idea
Then, How can you put a giraffe on the fridge?
Do the same thing on the elephant
Remove the elephant first then put the giraffe in
Chop it before putting it in
No idea
Lion invited all the animals in the world for his birthday party, which animal didn't attend
All of them
Other lions
Giraffe
Everybody attends
If you will be crossing a river full of crocodiles, how can you survive?
Use a boat, then paddle fast
Just swim ahead, all of the them are still on the party
Don't cross, you will die
Just ignore them and go home
How many sides does a circle has?
0
1
2
3
"No" Is what type of response?
A positive
A formal
A negative
A infromal
What word describes the sun when it lowers toward the horizon?
Dusk
Sundown
Sunset
Dawn
Sunrise
If I only like sandwiches with egg AND bacon. Do I like bacon sandwiches?
yes
no
it depends
If I like brown bread or white bread sandwiches, do I like tuna on white bread sandwiches?
yes
no
it depends
I will go to the party if Billy or Bob are there - will I go if only Billy is there?
yes
no
it depends
Which Logic word does this represent
AND
OR
NOT
XOR
What Logic operator does this represent?
OR
NOR
AND
NOT
If I don't like peas and nor do I like honey, do I like peas with chips and no honey?
yes
no
It depends
What is the next number in this sequence?
1,1,2,3,5,8 ____
14
13
11
8
I got a 94 on my test.
what conclusion can be made.
8:4 as 10:
