Mathematical Reasoning Test

Result

Mathematical Reasoning Test - 14

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Inverse of a statement can be explained as

A
Negating both the hypothesis and conclusion of a conditional statement.

B
Antecedent is the negation of the original antecedent and whose consequent is the negation of the original consequent.

C
both are correct

D
none is correct

Solution

Inverse of a statement means converting positive statement into a negative one.
In mathematical terms, by applying negation .
Since, option A and B means the same. Hence, option C is the answer.
Question 2
1 / -0

Which of the following is a statement?

A
Rani is a beautiful girl.

B
Shut the door.

C
Yesterday was Friday..

D
If its raining then there must be cloud in the sky.

Solution

If its raining then there must be cloud in the sky.

This a statement.
A statement is a closed sentence. It can also be a mathematical identity.
A statement should have a complete meaning independently.
Question 3
1 / -0

If a compound statement is made up of three simple statements, then the number of rows in the truth table is

A
$$8$$

B
$$6$$

C
$$4$$

D
$$2$$

Solution

Fact: If a compound statement is made up of $$n$$ simple statements, then number of rows in the truth table will be $$2^n$$

Here $$n=3$$ is given, so number of rows will be $$=2^3=8$$
Question 4
1 / -0

The converse of the contrapositive of the conditional $$ p \rightarrow \sim q $$ is :

A
$$ p \rightarrow q $$

B
$$ \sim p \rightarrow \sim q $$

C
$$ \sim q \rightarrow p $$

D
$$ \sim p \rightarrow q $$

Solution

The contrapositive of $$ p \rightarrow \sim q $$ is
$$ \sim (\sim q) \rightarrow \sim p $$ or $$ q \rightarrow \sim p $$
Also, converse of $$ q \rightarrow \sim p $$ is $$ \sim p \rightarrow q$$.
Hence, converse of the contrapositive of the conditional $$ p \rightarrow \sim q $$ is $$ \sim p \rightarrow q$$
Question 5
1 / -0

If truth values of $$p$$ be $$F$$ and $$q$$ be $$T$$. Then, truth value of $$\sim (\sim p\vee q)$$ is

A
$$T$$

B
$$F$$

C
Either $$T$$ or $$F$$

D
Neither $$T$$ not $$F$$

Solution

$$p$$ $$q$$ $$\sim p$$ $$\sim p\vee q$$ $$\sim (\sim p\vee q)$$
$$F$$ $$T$$ $$T$$ $$T$$ $$F$$
$$\therefore$$ Truth value of $$\sim (\sim p\vee q)$$ is F.
Question 6
1 / -0

Let $$p, q$$ and $$r$$ be any three logical statements. Which one of the following is true?

A
$$\sim [p \wedge (\sim q)] \equiv (\sim p )\wedge q$$

B
$$\sim (p \vee q) \wedge (\sim r) \equiv (\sim p) \vee (\sim q) \vee (\sim r)$$

C
$$\sim [p \vee (\sim q)] \equiv (\sim p) \wedge q$$

D
$$\sim [p \wedge (\sim q)] \equiv (\sim p) \wedge \sim q$$

E
$$\sim [p \wedge (\sim q)] \equiv p \wedge q$$

Solution

$$\sim [p\wedge (\sim q)]\equiv (\sim p)\vee \sim (\sim q)\equiv (\sim p)\vee q$$

So option $$A$$ is not correct

$$\sim (p\vee q)\wedge (\sim r)\equiv (\sim p)\wedge (\sim q)\wedge (\sim r)$$

So option $$B$$ is also not correct.
$$\sim [p\vee (\sim q)]\equiv (\sim p)\wedge \sim (\sim q)\equiv (\sim p)\wedge q$$

So option $$C$$ is correct.
Question 7
1 / -0

"If we control population growth, then we prosper". Negative of this proposition is:

A
If we do not control population growth, we prosper

B
If we control population, we do not prosper

C
we control population and we do not prosper

D
If we don't control population, we do not prosper

Solution

Given,
$$\text{"if we control population growth, then we prosper."}$$
Statement contain if......then proposition.

Let $$P=\text{we control population growth}$$ and $$Q=\text{we prosper}$$
statement=$$P\rightarrow{Q}$$
$$P\rightarrow{Q}$$ is equivalent to "$$\sim P \vee Q$$"

Therefore,
Negation of $$\sim P \vee Q$$ is "$$P \wedge \sim Q$$"

Now,
Negation of Statement:-
$$\text{"we control population growth and we do not prosper."}$$
Question 8
1 / -0

The converse of $$p\Rightarrow q$$ is

A
$$p\Rightarrow q$$

B
$$q\Rightarrow p$$

C
$$-p\Rightarrow -q$$

D
$$-q \Rightarrow -p$$

Solution

Suppose conditional statement of the form "If $$p$$ then $$q$$ is given.The converse is "If $$p$$ then $$q$$.
of $$p \implies q$$ is $$q \implies p$$ is converse
Question 9
1 / -0

Which one of the following statement is a tautology?

A
$$p\rightarrow (p\rightarrow q)$$

B
$$(p \vee p)\rightarrow q$$

C
$$p \vee (p\rightarrow q)$$

D
$$p \vee (q\rightarrow p)$$

Solution
Question 10
1 / -0

The negation of the statement $$(p\rightarrow q)\wedge r$$ is

A
$$p\wedge \sim q\vee \sim r$$

B
$$(\sim p\wedge q)\wedge (\sim r)$$

C
$$(p\wedge \sim q)\wedge (r)$$

D
$$(p\wedge \sim q)\wedge (\sim r)$$

Solution

$$p\rightarrow q$$
$$=\sim p\vee q---(1)$$
$$\sim [(p\rightarrow q)\wedge r]$$
$$\sim [\sim p\vee q\wedge r]$$...[form(i)]
$$\sim (\sim p\vee q)\vee \sim r$$...[Demorgans low]
$$\sim (\sim p)\wedge \sim q\vee q\sim r $$ $$ av(b\wedge c)$$
$$p\wedge \sim q\vee \sim r $$ $$ =(a\vee b)\vee (a\vee c)]$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

$$p$$	$$q$$	$$\sim p$$	$$\sim p\vee q$$	$$\sim (\sim p\vee q)$$
$$F$$	$$T$$	$$T$$	$$T$$	$$F$$

Mathematical Reasoning Test - 14

Result

Mathematical Reasoning Test - 14

Score

-

Rank

-

SHARING IS CARING

Question 1

Negating both the hypothesis and conclusion of a conditional statement.

Antecedent is the negation of the original antecedent and whose consequent is the negation of the original consequent.

both are correct

none is correct

Solution

Question 2

Rani is a beautiful girl.

Shut the door.

Yesterday was Friday..

If its raining then there must be cloud in the sky.

Solution

Question 3

$$8$$

$$6$$

$$4$$

$$2$$

Solution

Question 4

$$ p \rightarrow q $$

$$ \sim p \rightarrow \sim q $$

$$ \sim q \rightarrow p $$

$$ \sim p \rightarrow q $$

Solution

Question 5

$$T$$

$$F$$

Either $$T$$ or $$F$$

Neither $$T$$ not $$F$$

Solution

Question 6

$$\sim [p \wedge (\sim q)] \equiv (\sim p )\wedge q$$

$$\sim (p \vee q) \wedge (\sim r) \equiv (\sim p) \vee (\sim q) \vee (\sim r)$$

$$\sim [p \vee (\sim q)] \equiv (\sim p) \wedge q$$

$$\sim [p \wedge (\sim q)] \equiv (\sim p) \wedge \sim q$$

$$\sim [p \wedge (\sim q)] \equiv p \wedge q$$

Solution

Question 7

If we do not control population growth, we prosper

If we control population, we do not prosper

we control population and we do not prosper

If we don't control population, we do not prosper

Solution

Question 8

$$p\Rightarrow q$$

$$q\Rightarrow p$$

$$-p\Rightarrow -q$$

$$-q \Rightarrow -p$$

Solution

Question 9

$$p\rightarrow (p\rightarrow q)$$

$$(p \vee p)\rightarrow q$$

$$p \vee (p\rightarrow q)$$

$$p \vee (q\rightarrow p)$$

Solution

Question 10

$$p\wedge \sim q\vee \sim r$$

$$(\sim p\wedge q)\wedge (\sim r)$$

$$(p\wedge \sim q)\wedge (r)$$

$$(p\wedge \sim q)\wedge (\sim r)$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.