Mathematical Reasoning Test

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Mathematical Reasoning Test - 12

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Question 1
1 / -0

Which of the following is the converse of the statement: "If x>4 then x+2>5"?

A
If x+2<5 then x<4

B
If x is not greater than 4 then x+2 is not greater than 5

C
If x+2>5 then x>4

D
If x+2 is not greater than 5 then x is not greater than 4

Solution

Converse of "If $$A$$ then $$B$$" is "If $$B$$ then $$A$$". Hence,
Converse of "If $$x>4$$ then $$x+2>5$$" will be "If $$x+2>5$$ then $$x>4$$"
So, $$C$$ is correct.
Question 2
1 / -0

When $$y=3$$ which of the following is FALSE?

A
$$y$$ is prime and $$ y$$ is odd

B
$$y$$ is odd or $$y$$ is even

C
$$y$$ is not prime and $$y$$ is odd

D
$$y$$ is odd and $$2y$$ is even

Solution

Remember what is True: $$3$$ is prime, odd and $$2(3)$$ is even
Choice 1 : T and T is TRUE
Choice 2 : T or F is TRUE
Choice 3 : F and T is FALSE
Choice 4 : T and T is TRUE
Question 3
1 / -0

"If Deb and Sam go to the mall then it is snowing"
Which statement below is logically equivalent?

A
If Deb and Sam do not go to the mall then it is not snowing

B
If Deb and Sam do not go to the mall them it is snowing

C
If it is snowing then Deb and Sam go to the mall

D
If it is not snowing then Deb and Sam do not go to the mall

Solution

Deb and Sam go to the mall only if it is snowing which means if it is not snowing, they don't go to the mall.
So, $$D$$ is correct.
Question 4
1 / -0

Which of the following statements is the converse of "If the moon is full, then the vampires are prowling."?

A
If the vampires are prowling, then the moon is full.

B
If the moon is not full, then the vampires are prowling

C
If the vampires are not prowling, then the moon is not full.

D
None of these

Solution

Converse of "If $$P$$, then $$Q$$" is "If $$Q$$, then $$P$$"
Similarly, option "$$A$$" is converse of the given statement "If the moon is full, then the vampires are prowling."
Question 5
1 / -0

Which is logically equivalent to "If today is Sunday Matt cannot play hockey"?

A
Today is Sunday and Matt can play hockey

B
If Matt plays hockey then today is not Sunday

C
Today is Sunday and Matt cannot play hockey

D
Today is not Sunday if and only if Matt plays hockey

Solution

Matt can play Hockey on any day other than Sunday.
Hence, $$B$$ is correct.
Question 6
1 / -0

Which statement is logically equivalent to "If Yoda cannot use a lightsaber then he cannot help Luke win the battle"

A
Yoda cannot use a lightsaber and he will help Luke win the battle

B
If Yoda can help Luke win the battle then he can use a lightsaber

C
Yoda can use a lightsaber if and only if he can help Luke win the battle

D
Yoda cannot use a lightsaber and will not help Luke win the battle

Solution

A statement is logically equivalent to its contrapositive To form the contrapositive switch the "If" and "then" sections of the statement AND insert "NOTs" into each section Notice in this situation that inserting "NOTs" turns the thoughts positive (you are negating negative thoughts)
Question 7
1 / -0

Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.

A
If you lose the game then you dont know the rules or you are overconfident.

B
A sufficient condition that you win the game is that you know the rules or you are not overconfident.

C
If you dont know the rules or are overconfident you lose the game

D
If you know the rules and are overconfident then you win the game.

Solution

Contrapositive is the inverse of the converse of the statement.
It is obtained by first interchanging the hypothesis and conclusion and then adding "not" to both
In this case, converse is "If you win the game, then you know the rules but are not overconfident."
Inverse of this statement gives answer as A.
Question 8
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 these

Solution

The given statement can be written as ''If there is a thunderstorm, then our pond floods".
Inverse of a given statement is "If our pond does not flood, then we did not get a thunderstorm.".
"If our pond does not flood, then we did not get a thunderstorm.".
Hence, option C is correct.
Question 9
1 / -0

$$\sim \left[ \left( p\wedge q \right) \rightarrow \left( \sim p\vee q \right) \right]$$ is

A
Tautology

B
Contradiction

C
Neither (A) nor (B)

D
Either (A) or (B)

Solution

It is clear from the table that
$$\sim \left[\left( p\wedge q \right) \rightarrow \left( \sim p\vee q \right)\right] $$
is a contradiction.
Question 10
1 / -0

Which of the following statements is the converse of "You cannot skateboard if you do not have a sense of balance."?

A
If you cannot skateboard, then you do not have a sense of balance.

B
If you do not have a sense of balance, then you cannot skateboard.

C
If you skateboard, then you have a sense of balance.

D
None of these

Solution

Converse of "If $$P$$, then $$Q$$" is "If $$Q$$, then $$P$$".
Now, the given statement "You cannot skateboard if you do not have a sense of balance." can be re-written as "If you do not have a sense of balance, then you cannot skateboard."
The converse of this statement is option $$B$$.

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Re-Attempt Weekly Quiz Competition

Mathematical Reasoning Test - 12

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Mathematical Reasoning Test - 12

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SHARING IS CARING

Question 1

If x+2<5 then x<4

If x is not greater than 4 then x+2 is not greater than 5

If x+2>5 then x>4

If x+2 is not greater than 5 then x is not greater than 4

Solution

Question 2

$$y$$ is prime and $$ y$$ is odd

$$y$$ is odd or $$y$$ is even

$$y$$ is not prime and $$y$$ is odd

$$y$$ is odd and $$2y$$ is even

Solution

Question 3

If Deb and Sam do not go to the mall then it is not snowing

If Deb and Sam do not go to the mall them it is snowing

If it is snowing then Deb and Sam go to the mall

If it is not snowing then Deb and Sam do not go to the mall

Solution

Question 4

If the vampires are prowling, then the moon is full.

If the moon is not full, then the vampires are prowling

If the vampires are not prowling, then the moon is not full.

None of these

Solution

Question 5

Today is Sunday and Matt can play hockey

If Matt plays hockey then today is not Sunday

Today is Sunday and Matt cannot play hockey

Today is not Sunday if and only if Matt plays hockey

Solution

Question 6

Yoda cannot use a lightsaber and he will help Luke win the battle

If Yoda can help Luke win the battle then he can use a lightsaber

Yoda can use a lightsaber if and only if he can help Luke win the battle

Yoda cannot use a lightsaber and will not help Luke win the battle

Solution

Question 7

If you lose the game then you dont know the rules or you are overconfident.

A sufficient condition that you win the game is that you know the rules or you are not overconfident.

If you dont know the rules or are overconfident you lose the game

If you know the rules and are overconfident then you win the game.

Solution

Question 8

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 these

Solution

Question 9

Tautology

Contradiction

Neither (A) nor (B)

Either (A) or (B)

Solution

Question 10

If you cannot skateboard, then you do not have a sense of balance.

If you do not have a sense of balance, then you cannot skateboard.

If you skateboard, then you have a sense of balance.

None of these

Solution

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