Mathematical Reasoning Test

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Mathematical Reasoning Test - 25

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Question 1
1 / -0

The inverse of " If two angles are congruent, then they have the same measure" is

A
If two angles have the same measure, then they are congruent.

B
If two angles are not congruent, then they do not have the same measure.

C
If two angles do not have the same measure, then they are not congruent.

D
None of these

Solution

It the statement/ fact is"If two angles are congruent, then they have the same measure" then its inverse will be
" If two angles do not have the same measure then they are not congruent"
Question 2
1 / -0

"If A is true, then B is false", is logically equivalent to which of the following?
I. If A is false, then B is true.
II. If B is false, then A is true.
III. If B is true, then A is false

A
None of the above

B
III only

C
I and II only

D
II and III only

E
I, II and III

Solution

Given if A is true ,then B is false
(I) if A is false ,then B is true not possible because A not logical repleted to B
(II) if B is false ,then A is true not possible because B not logical repleted to A
(III)If A is true then B is false, but then A is false. Which means B is true, but then A is true. Which means B is false.
Then (III) is write
Question 3
1 / -0

The inverse of the statement " if Abbey is not injured, she will win the race." is

A
If Abbey is injured, she will not win the race.

B
If Abbey is not injured, she will not win the race."

C
If Abbey is injured, she will win the race."

D
None of these

Solution

The inverse of statement is when the meaning of statement does not change.
Inverse of statement :- If Abbey is injured , she will not win the race.
Where the meaning of statement doesn't change.
Question 4
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The inverse of statement is " If you grew in Alaska, then you have seen snow."

A
"If you did not grow up in Alaska, then you have not seen snow."

B
"If you grow up in Alaska, then you have not seen snow."

C
"If you did not grow up in Alaska, then you have seen snow."

D
None of these

Solution

The inverse of a statement is when you write negative of statement without changing the actual meaning of statement.
The inverse of “If p then q” is "If $$\text{~p}$$ then $$\text{~q}$$." in the solution
In statement 'If you grew in Alaska ,then you have seen snow'.
Inverse :- 'If you did not grow up in Alaska, then you have not seen snow'.
Question 5
1 / -0

The inverse of statement "If a dog is barking, then it will not bite" is

A
If a dog is not barking, then it will bite.

B
If a dog is biting, then it will not bark.

C
If a dog is not biting, then it will not bark.

D
None of the above

Solution

The inverse of statement without changing meaning of statement
statement becomes 'If a dog is not barking, then it will bite".
Question 6
1 / -0

Which of the following statements is the inverse of
"Our pond floods whenever there is a thunderstorm."?

A
If there is a thunderstorm, then our pond floods.

B
If we do not get a thunderstorm, then our pond does not flood.

C
If our pond does not flood, then we did not get a thunderstorm.

D
None of the above

Solution

The inverse of statement is when the meaning of statement does not change.
Inverse of statement :- If we do not get a thunderstorm, then our pond does not flood.
Where the meaning of statement doesn't change.
Question 7
1 / -0

Which of the following statements is the inverse of
"If you do not understand geometry, then you do not know how to reason deductively." ?

A
If you reason deductively, then you understand geometry.

B
If you understand geometry, then you reason deductively.

C
If the do not reason deductively, then you understand geometry.

D
None of the above

Solution

The inverse of statement is when the meaning of statement does not change.
Inverse of statement :- If you understand geometry, then you reason deductively.
Where the meaning of statement doesn't change.
Question 8
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Which statement represents the inverse of the statement "If it is snowing, then Skeeter wears a sweater."?

A
If Skeeter wears a sweater, then it is snowing.

B
If Skeeter does not wear a sweater, then it is not snowing.

C
If it is not snowing, then Skeeter does not wear a sweater.

D
If it is not snowing, then Skeeter wears a sweater.

Solution

To find the inverse we need to negate the hypothesis and conclusion, and hence on negating it is snowing we get it is not snowing and on negating skeeter wears a sweater we get skeeter does not wear a sweater.
$$C$$
Question 9
1 / -0

If $$x+4=8$$, then $$x=4$$, Inverse of the statement is-

A
If $$x+4=8$$, then $$x\neq4$$

B
If $$x+4\neq8$$, then $$x\neq4$$

C
If $$x+4\neq8$$, then $$x=4$$

D
none of the above

Solution

$$x+4\neq8$$, then $$x\neq4$$
this is the inverse obtained by negating hypothesis and conclusion condition
Question 10
1 / -0

Write negation of:
All natural numbers are integers and all integers are not natural numbers.

A
All natural numbers are not integers and all integers are not natural numbers.

B
All natural numbers are integers and all integers are natural numbers.

C
Some natural numbers are integers and all integers are not natural numbers.

D
All natural numbers are not integers and some integers are natural numbers.

Solution

the negation of
All natural numbers are integers and all integers are not natural numbers. is All natural numbers are not integers and some integers are natural numbers. or Some natural numbers are not integers and some integers are natural numbers
more or less option d is correct.
$$D$$

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Mathematical Reasoning Test - 25

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Mathematical Reasoning Test - 25

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Question 1

If two angles have the same measure, then they are congruent.

If two angles are not congruent, then they do not have the same measure.

If two angles do not have the same measure, then they are not congruent.

None of these

Solution

Question 2

None of the above

III only

I and II only

II and III only

I, II and III

Solution

Question 3

If Abbey is injured, she will not win the race.

If Abbey is not injured, she will not win the race."

If Abbey is injured, she will win the race."

None of these

Solution

Question 4

"If you did not grow up in Alaska, then you have not seen snow."

"If you grow up in Alaska, then you have not seen snow."

"If you did not grow up in Alaska, then you have seen snow."

None of these

Solution

Question 5

If a dog is not barking, then it will bite.

If a dog is biting, then it will not bark.

If a dog is not biting, then it will not bark.

None of the above

Solution

Question 6

If there is a thunderstorm, then our pond floods.

If we do not get a thunderstorm, then our pond does not flood.

If our pond does not flood, then we did not get a thunderstorm.

None of the above

Solution

Question 7

If you reason deductively, then you understand geometry.

If you understand geometry, then you reason deductively.

If the do not reason deductively, then you understand geometry.

None of the above

Solution

Question 8

If Skeeter wears a sweater, then it is snowing.

If Skeeter does not wear a sweater, then it is not snowing.

If it is not snowing, then Skeeter does not wear a sweater.

If it is not snowing, then Skeeter wears a sweater.

Solution

Question 9

If $$x+4=8$$, then $$x\neq4$$

If $$x+4\neq8$$, then $$x\neq4$$

If $$x+4\neq8$$, then $$x=4$$

none of the above

Solution

Question 10

All natural numbers are not integers and all integers are not natural numbers.

All natural numbers are integers and all integers are natural numbers.

Some natural numbers are integers and all integers are not natural numbers.

All natural numbers are not integers and some integers are natural numbers.

Solution

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