Free Printable Mathematical Logic

1.

$\left(p\wedge q\right)\rightarrow r\$ is logically equivalent to

a)

$p\rightarrow\left(q\rightarrow r\right)$

b)

$\left(p\wedge q\right)\rightarrow\sim r$

c)

$\left(\sim p\vee\sim q\right)\rightarrow\sim r$

d)

$\left(p\vee q\right)\rightarrow r$

2.

The negation of $p\wedge\left(q\rightarrow r\right)$ is

a)

$\sim p\wedge\left(\sim q\rightarrow\sim r\right)$

b)

$p\vee\left(\sim q\vee r\right)$

c)

$\sim p\wedge\left(\sim q\rightarrow\sim r\right)$

d)

$\sim p\vee\left(\sim q\wedge\sim r\right)$

3.

Examine $\left(p\wedge q\right)\wedge\left(\sim p\vee\sim q\right)$

a)

Tautology

b)

Contradiction

c)

Contingency

d)

None of these

4.

Dual of $\left(p\wedge t\right)\vee\left(c\wedge\sim q\right)$

a)

$\left(p\vee c\right)\wedge\left(t\wedge q\right)$

b)

$\left(p\vee c\right)\wedge\left(c\wedge\sim q\right)$

c)

$\left(p\wedge c\right)\vee\left(t\wedge q\right)$

d)

$\left(p\vee c\right)\wedge\left(t\vee\sim q\right)$

5.

7>3 and 4 >11 Negation of Statement is

a)

$7<3\ or\ 4<11$

b)

$7\le3\ and\ 4\le11$

c)

$7\le3\ or\ 4\le11$

d)

$7\ne3\ and\ 4\ne11$

6.

"If a Function is differentiable then it is Continuous."What is Contra-positive of Statement .

a)

If a function is not continuous then it is not differentiable

b)

If a function is not differentiable then it is not continuous.

c)

If a function is continuous then it is differentiable

d)

If a function is not continuous then it is differentiable.

7.

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

a)

If I do not have a Siberian Husky, then I do not have a dog.

b)

If I have a dog, then I have a Siberian Husky.

c)

If I do not have a dog, then I do not have a Siberian Husky.

d)

If I do not have a Siberian Husky, then I have a dog.

8.

If $p$ and $q$ are two statements, then statement $p\longrightarrow q\ \wedge\sim q$ is

a)

Tautology

b)

Contradiction

c)

Neither Tautology nor contradiction

d)

None of the above

9.

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.......

a)

Commutative Law

b)

Associative law

c)

De-Morgan's Law

d)

Distributive Law

10.

Truth value of the statement "if p then q" is false when

a)

p is true, q is true

b)

p is true, q is false

c)

p is false, q is true

d)

p is false, q is false

11.

Which of the following is the statement?

a)

May you live long !

b)

May God bless you !

c)

The Sun is star

d)

Hurrah ! We have won the match

12.

Which of the following is not the statement?

a)

Where are you going?

b)

8 is less than 6

c)

The sum of interior angles of a triangles is 180 degrees

d)

Every set is a finite set

13.

For any two statements p and q, the negation of the expression $p\vee\left(\sim p\wedge q\right)$ is

a)

$\sim p\ \vee\sim q$

b)

$\sim p\ \wedge\sim q$

c)

$p\wedge q$

d)

$p\longleftrightarrow q$

14.

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

b)

Ram is not in class X but Rashmi is not in class XII

c)

Either Ram is not in class X or Ram is not in class XII

d)

None of these

15.

Which of the following is logically equivalent to $\sim(p\longleftrightarrow q)$

a)

$\sim p∧\sim\ q$

b)

$\sim p∨\sim q$

c)

$(p∧\sim q)∨(\sim p∧q)$

d)

None of these

16.

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.

a)

$\sim(p∧q)\longrightarrow(r∧s)$

b)

$\sim(p∧\sim q)\longrightarrow(r∧s)$

c)

$\sim(p∧q)\longrightarrow(r∨s)$

d)

None of these

17.

Which of the following is true

a)

$p\longrightarrow q≡\sim p\longrightarrow\sim q$

b)

$\sim(p\longrightarrow\sim q)≡\sim p∧q$

c)

$\sim(\sim p\longrightarrow\sim q)≡\sim p∧q$

d)

$\sim(p\longleftrightarrow q)≡\sim(p\longrightarrow q)∧\sim(q\longrightarrow p)$

18.

If $p\longrightarrow(\sim p∨q)$ is false, the truth values of p and q are respectively

a)

F, T

b)

F, F

c)

T, T

d)

T, F

19.

The false statement in the following is

a)

$p∧(\sim p)$ is a contradiction

b)

$(p\longrightarrow q)\longleftrightarrow(\sim q\longrightarrow\sim p)$ is a contradiction

c)

$(\sim p)\longleftrightarrow p$ is a tautology

d)

$p∨(\sim p)$ is a tautology

20.

If $p\longrightarrow(q∨r)$ is false, then the truth values of p, q, r are respectively

a)

T, F, F

b)

F, F, F

c)

F, T, T

d)

T, T, F

21.

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

b)

If a number is not a rational or not an irrational, then it is not real

c)

If a number is not real, then it is neither rational nor irrational

d)

If a number is real, then it is rational or irrational

22.

If p, q, r are simple propositions, then $(p∧q)∧(q∧r)$ is true then

a)

p, q, r are all false

b)

p is true and q and r are false

c)

p, q are true and r is false

d)

p, q, r are all true

23.

If $(p∧\sim r)\longrightarrow(q∨r)$ is false and q and r are both false, then p is

a)

True

b)

False

c)

May be true or false

d)

Data insufficient

24.

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

a)

True if q is true

b)

False

c)

True if r is false

d)

True

25.

$p\longrightarrow q$

can also be written as

a)

$p\longrightarrow\sim q$

b)

$\sim p∨q$

c)

$\sim q\longrightarrow\sim p$

d)

None of these

26.

p: Ram is coward

q: ram is lazy

r: ram is rich

Identify statement for "It is not true that ram is not rich"

a)

$\sim p\vee\sim q$

b)

$\sim p\vee\sim r$

c)

$\sim(\sim r)$

d)

$\sim(\sim q)$

27.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

a)

If a polygon is not a quadrilateral, then it is not a trapezoid.

b)

If a polygon is not a trapezoid, then it is not a quadrilateral.

c)

If a polygon is a trapezoid, then it is a quadrilateral.

d)

A rectangle is also a quadrilateral.

28.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

a)

If a polygon is a trapezoid, then it is a quadrilateral.

b)

If a polygon is not a quadrilateral, then it is not a trapezoid.

c)

If a polygon is not a trapezoid, then it is not a quadrilateral.

d)

A rectangle is also a quadrilateral.

29.

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)

a → b

b)

b→ a

c)

a → ~ b

d)

~a → ~ b

30.

Given-

p is TRUE

q is FALSE

Which of the following statements is FALSE?

a)

$p\wedge\sim q$

b)

$\sim\left(q\right)$

c)

$p\rightarrow q$

d)

$p\vee q$

Mathematical Logic

Total questions: 30

Worksheet time: 30mins

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