Mathematical Reasoning Test

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Mathematical Reasoning Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is the inverse of "If it rains, then I do not go fishing."?

A
If I go fishing, then it does not rain.

B
If I do not go fishing, then it rains.

C
If it does not rain, then I go fishing.

D
None of these

Solution

Therefore, the reason comes after the assertion.
Then, the inverse of the expression "if it rains, then I do not go fishing " is:
If I go fishing, then it does not rain
Question 2
1 / -0

The negative of the statement "he is rich and happy" is given by

A
He is not rich and not happy

B
He is not rich or not happy

C
He is rich and happy

D
He is not rich and happy

Solution

The negation of the given statement is "he is not rich or not happy".
Question 3
1 / -0

The inverse of the statement "If it is raining then the grass is wet"

A
"If it is not raining then the grass is not wet".

B
"If it is raining then the grass is not wet".

C
"If it is not raining then the grass is wet".

D
None of these

Solution

$$p\rightarrow{q}$$
Inverse is $$\sim{p}\rightarrow\sim{q}$$
$$\Rightarrow$$ Inverse of :
It it is raining then the grass is wet.
is:
If it is not raining then the grass is not wet.
Question 4
1 / -0

If p : A man is happy
q : A man is rich
Then, the statement, "If a man is not happy, then he is not rich" is written as

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

B
$$\sim q\rightarrow p$$

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

D
$$q\rightarrow \sim p$$

Solution

Given, p : A man is happy
and q : A man is rich
'If a man is not happy, then he is not rich' is written as $$\sim p \rightarrow \sim q$$.
Question 5
1 / -0

Which of the following statements is logically equivalent to "The solution is easy if you read the question carefully."?

A
If you do not read the question carefully, the solution is hard.

B
If the solution is easy, then you read the question carefully.

C
If the solution is hard, then you did not read the question carefully.

D
None of these

Solution

Given Statement:
The solution is easy if you read the question carefully.

Logically equivalent statement:
If you do not read the question carefully, the solution is hard.
Question 6
1 / -0

The inverse of the statement " If a person is mean, then they are a fighter " is-

A
If a person is not mean, then they are not a fighter.

B
If a person is not mean, then they are a fighter.

C
If a person is mean, then they are not a fighter.

D
None of the above

Solution

A person is not mean is the negation of the hypothesis that a person is mean and they are not a fighter is the negation of the conclusion they are a fighter.
$$A$$
Question 7
1 / -0

Negation of the statement "Every natural number is an integer".

A
All natural numbers are whole numbers.

B
Every natural number is not an integer.

C
Every natural number is not a real number.

D
none of the above

Solution

Negation of "Every Natural number is an integer." is "Every Natural number is NOT an integer."
Question 8
1 / -0

The inverse of the statement "If a number is divisible by 4 then it is also divisible by 2" is-

A
If a number is divisible by 4, then it is always divisible by 2.

B
If a number is not divisible by 4, then it is divisible by 2.

C
If a number is not divisible by 4, then it is not divisible by 2.

D
None of the above

Solution

a number is not divisible by 4 is the negation of the hypothesis a number is divisible by 4 ,and it is not divisible by 2 is the negation of the conclusion it is also divisible by 2
Question 9
1 / -0

Inverse of the statement "If the triangle with side lengths $$a, b, c$$ is a right triangle, then $$a^2 + b^2 = c^2$$.

A
If $$a^2+b^2\neq c^2$$ then the triangle with side lengths $$a, b, c$$ is not a right triangle.

B
If $$a^2+b^2 = c^2$$ then the triangle with side lengths $$a, b, c$$ is a right triangle.

C
If the triangle with side lengths $$a,b,c$$ is a not right triangle, then $$a^2 + b^2 \neq c^2$$.

D
None of the above.

Solution

Given,
If the triangle with side lengths $$a, b, c$$ is a right triangle, then $$a^2+b^2=c^2$$
This is of the form $$p\rightarrow{q}$$
$$p$$: If the triangle with side lengths $$a, b, c$$ is a right triagle.
$$q: a^2+b^2=c^2$$
Inverse of $$p\rightarrow{q}$$ is $$\sim{p}\rightarrow\sim{q}$$
$$\Rightarrow$$ If the triangle with side lengths $$a, b, c $$ is not a right triangle, then $$a^2+b^2=c^2$$.
Question 10
1 / -0

Write the inverse of the statement-
If you do not drink your milk, you will not be strong.

A
If you are strong, then you drink your milk,

B
If you do not drink your milk, then you are strong.

C
If you drink your milk, then you are strong.

D
None of the above

Solution

If you drink your milk is negation of the hypothesis if you donot drink your milk you are strong is negation of the conclusion you will not be strong.
$$C$$

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Mathematical Reasoning Test - 13

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Mathematical Reasoning Test - 13

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Question 1

If I go fishing, then it does not rain.

If I do not go fishing, then it rains.

If it does not rain, then I go fishing.

None of these

Solution

Question 2

He is not rich and not happy

He is not rich or not happy

He is rich and happy

He is not rich and happy

Solution

Question 3

"If it is not raining then the grass is not wet".

"If it is raining then the grass is not wet".

"If it is not raining then the grass is wet".

None of these

Solution

Question 4

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

$$\sim q\rightarrow p$$

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

$$q\rightarrow \sim p$$

Solution

Question 5

If you do not read the question carefully, the solution is hard.

If the solution is easy, then you read the question carefully.

If the solution is hard, then you did not read the question carefully.

None of these

Solution

Question 6

If a person is not mean, then they are not a fighter.

If a person is not mean, then they are a fighter.

If a person is mean, then they are not a fighter.

None of the above

Solution

Question 7

All natural numbers are whole numbers.

Every natural number is not an integer.

Every natural number is not a real number.

none of the above

Solution

Question 8

If a number is divisible by 4, then it is always divisible by 2.

If a number is not divisible by 4, then it is divisible by 2.

If a number is not divisible by 4, then it is not divisible by 2.

None of the above

Solution

Question 9

If $$a^2+b^2\neq c^2$$ then the triangle with side lengths $$a, b, c$$ is not a right triangle.

If $$a^2+b^2 = c^2$$ then the triangle with side lengths $$a, b, c$$ is a right triangle.

If the triangle with side lengths $$a,b,c$$ is a not right triangle, then $$a^2 + b^2 \neq c^2$$.

None of the above.

Solution

Question 10

If you are strong, then you drink your milk,

If you do not drink your milk, then you are strong.

If you drink your milk, then you are strong.

None of the above

Solution

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