Mathematical Reasoning Test

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Mathematical Reasoning Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

The compound statement, "If you want to top the school, then you do not study hard" is equivalent to

A
"If you want to top the school, then you need to study hard".

B
"If you will not top in the school, then you study hard".

C
"If you study hard, then you will not top the school".

D
"If you do not study hard, then you will top in the school".

Solution

An equivalent statement of a compound statement, has the same meaning as the compound statement.

So, for the given compound statement, the equivalent statement is " If you study hard, then you will not top the school. "
Question 2
1 / -0

Which of the following is equivalent to $$p\Longleftrightarrow q$$?

A
$$p\implies q$$

B
$$q\implies p$$

C
$$(p\implies q)\wedge(q\implies p)$$

D
None of these

Solution

The truth values of $$ p\Longleftrightarrow q $$ are equal to the truth values of $$ (p\Longrightarrow q)\wedge (q\Longrightarrow p) $$

So, they are equivalent.
Question 3
1 / -0

The property $$p\wedge(q\vee r)\equiv(p\wedge q)\vee(p\wedge r)$$ is called

A
associative law

B
commutative law

C
distributive law

D
idempotent law

Solution

As the symbol AND $$ \wedge $$ is distributed over OR $$ \vee $$ , the given property is also called Distributive property.
Question 4
1 / -0

Write the negation of the statement "If the switch is on, then the fan rotates".

A
"If the switch is not on, then the fan does not rotate".

B
"If the fan does not rotate, then the switch is not on".

C
"The switch is not on or the fan rotates".

D
"The switch is on and the fan does not rotate".

Solution

To find the negation of the statement, we find the opposite of the conclusion.

So, negation of the given statement is " If the switch is on, then the fan does not rotate"
Question 5
1 / -0

The negation of the statement, "I go to school everyday", is

A
I never go to school.

B
Some days, I do not go to school.

C
Not all the days I do not go to school.

D
All days I go to school.

Solution

The negation or the opposite of the statement, " I go to school everyday" will be "Some days, I do not go to school" as there is a possibility of not going to school on some days rather than not going at all.
Question 6
1 / -0

In the above network, current flows from N to T when

A
p closed, q closed, r opened and s opened.

B
p dosed, q opened, s closed and r opened.

C
q closed, p opened, r opened and s closed.

D
p opened, q opened, r closed and s closed.

Solution

We can notice that current will flow from M to T, if atleast one of the pair of switches $$ q ; s $$ or $$ p ; r $$ are closed.

So, from the given options , the right option is q closed , open , r opened and s closed
Question 7
1 / -0

Find the converse of the statement, "If ABCD is square, then it is a rectangle".

A
If ABCD is a square, then it is .not a rectangle.

B
If ABCD is not a square, then i is a rectangle.

C
if ABCD is a rectangle, then it is square.

D
If ABCD is not a square, then it is not a rectangle.

Solution

In the converse of a statement, we reverse the statements such that the meaning does not change.
So converse of the given statement is " If ABCD is a rectangle, then it is a square"
Question 8
1 / -0

The counter example of the statement, "All odd numbers are primes", is

A
7

B
5

C
9

D
All the above

Solution

To prove the statement "All odd numbers are primes" we have to find an odd number which is not prime."

For example, $$ 9 $$ is an odd number which is not prime.
Question 9
1 / -0

If "All odd numbers are primes and the sum of three angles in a triangle is $$190^\circ$$", then "All odd numbers are primes or the sum of the angles in a triangle is $$190^\circ$$" is a

A
tautology

B
contradiction

C
contingency

D
not a statement

Solution

Both the statements are false as all odd numbers are primes and the sum of three angles of a triangle is not $$ 190^o $$
A tautology is a statement that is always true. And Two false statements make a True statement in a Tautology.
Question 10
1 / -0

In the above network, current flows from M to N, when

A
q closed, r opened and p closed.

B
q opened, p opened and r closed.

C
q opened, p closed and r closed.

D
q closed, p closed and r opened.

Solution

We can notice that current will flow from M to N, if atleast one of the switches $$ q $$ or $$ p $$ is closed and $$ r $$ is surely closed.

SO, from the given option is , the right option is q opened, p closed, , r closed

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Re-Attempt Weekly Quiz Competition

Mathematical Reasoning Test - 20

Result

Mathematical Reasoning Test - 20

Score

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Rank

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SHARING IS CARING

Question 1

"If you want to top the school, then you need to study hard".

"If you will not top in the school, then you study hard".

"If you study hard, then you will not top the school".

"If you do not study hard, then you will top in the school".

Solution

Question 2

$$p\implies q$$

$$q\implies p$$

$$(p\implies q)\wedge(q\implies p)$$

None of these

Solution

Question 3

associative law

commutative law

distributive law

idempotent law

Solution

Question 4

"If the switch is not on, then the fan does not rotate".

"If the fan does not rotate, then the switch is not on".

"The switch is not on or the fan rotates".

"The switch is on and the fan does not rotate".

Solution

Question 5

I never go to school.

Some days, I do not go to school.

Not all the days I do not go to school.

All days I go to school.

Solution

Question 6

p closed, q closed, r opened and s opened.

p dosed, q opened, s closed and r opened.

q closed, p opened, r opened and s closed.

p opened, q opened, r closed and s closed.

Solution

Question 7

If ABCD is a square, then it is .not a rectangle.

If ABCD is not a square, then i is a rectangle.

if ABCD is a rectangle, then it is square.

If ABCD is not a square, then it is not a rectangle.

Solution

Question 8

7

5

9

All the above

Solution

Question 9

tautology

contradiction

contingency

not a statement

Solution

Question 10

q closed, r opened and p closed.

q opened, p opened and r closed.

q opened, p closed and r closed.

q closed, p closed and r opened.

Solution

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