Mathematical Reasoning Test

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Mathematical Reasoning Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following connectives can be used for describing a switching network?

A
$$\vee$$

B
$$\wedge$$

C
Both (1) and (2)

D
None of these

Solution

We can use both AND $$ \wedge $$ to denote Series networks and OR $$ \vee $$ to denote Parallel networks to describe a switching network.
Question 2
1 / -0

"No square of a real number is less than zero" is equivalent to

A
for every real number a, $$a^2$$ is non negative.

B
$$\forall a\in R$$, $$a^2\ge0$$.

C
either (1) or (2).

D
None of these

Solution

Both the options $$ 1 $$ and $$ 2 $$ are correct, as option $$ 1 $$ has the statement rewritten with the same words as the original statement and option $$ 2 $$ has the statement written in mathematical way.
Question 3
1 / -0

Find the truth value of the statement, "The sum of any two odd numbers is an odd number".

A
True

B
False

C
Neither True nor False

D
Cannot be determined

Solution

Let us take two odd numbers to check the statement.

$$ 5 + 3 = 8 $$
$$ 7 + 5 = 12 $$

We notice that sum of two odd numbers is an even number.

Hence te given statement is False.
Question 4
1 / -0

The truth value of the statement, "We celebrate our Independence day on 15 August", is

A
T

B
F

C
neither T nor F

D
Cannot be determined

Solution

The given statement is True as we do celebrate our Independence day on $$ 15th $$ August.
Question 5
1 / -0

What is the truth value of the statement $$2\times3=6$$ or $$5+8=10$$?

A
True

B
False

C
Neither True nor False

D
Cannot be determined

Solution

The first statement $$ 2 \times 3 = 6 $$ is True.
But the second statement $$ 5 + 8 = 10 $$ is False.

Since the statements are connected using OR, the result will be True, if anyone of them is True.

Hence, truth value of the given statement is T.
Question 6
1 / -0

The converse of converse of the statement $$p\implies\sim q$$ is

A
$$\sim q\implies p$$

B
$$\sim p\implies q$$

C
$$p\implies\sim q$$

D
$$\sim q\implies\sim p$$

Solution

Converse of a converse of a statement will result in the original statement itself.

Hence, the answer is $$ p\Longrightarrow \sim q $$ which is the original statement itself.
Question 7
1 / -0

Which of the following connectives satisfy commutative law?

A
$$\wedge$$

B
$$\vee$$

C
$$\Leftrightarrow$$

D
All the above

Solution

All the three given symbols satisfy the commutative law.

$$ p\wedge q\Leftrightarrow q\wedge p $$
$$p\vee q\Leftrightarrow q\vee p$$
$$(p\Leftrightarrow q)\Leftrightarrow (q\Leftrightarrow p)$$
Question 8
1 / -0

In which of the following cases, $$p\Leftrightarrow q$$ is true?

A
p is true, q is true.

B
p is false, q is true.

C
p is true, q is false.

D
None of these.

Solution

As p is equivalent to q, the statement is true only when both are true.
Question 9
1 / -0

Write the compound statement, "If p, then q and if q, then p" in symbolic form.

A
$$(p\wedge q)\wedge(q\wedge p)$$

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

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

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

Solution

Then is denoted by the symbol $$ \Longrightarrow $$ and AND is denoted by the symbol $$ \wedge $$

So, the given statement can be denoted in symbolic form as $$ (q\Longrightarrow p)\wedge (p\Longrightarrow q) $$
Question 10
1 / -0

When does the truth value of the statement $$(p\vee r)\Leftrightarrow (q\vee r)$$ become true?

A
p is true, q is true.

B
p is false, q is false.

C
p is true, r is true.

D
Both (1) and (3)

Solution

As the LHS and RHS of the statements are equivalent, the statement will be true, when both $$ p $$ and $$ q $$ are either True or False.

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Mathematical Reasoning Test - 21

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Mathematical Reasoning Test - 21

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Question 1

$$\vee$$

$$\wedge$$

Both (1) and (2)

None of these

Solution

Question 2

for every real number a, $$a^2$$ is non negative.

$$\forall a\in R$$, $$a^2\ge0$$.

either (1) or (2).

None of these

Solution

Question 3

True

False

Neither True nor False

Cannot be determined

Solution

Question 4

T

F

neither T nor F

Cannot be determined

Solution

Question 5

True

False

Neither True nor False

Cannot be determined

Solution

Question 6

$$\sim q\implies p$$

$$\sim p\implies q$$

$$p\implies\sim q$$

$$\sim q\implies\sim p$$

Solution

Question 7

$$\wedge$$

$$\vee$$

$$\Leftrightarrow$$

All the above

Solution

Question 8

p is true, q is true.

p is false, q is true.

p is true, q is false.

None of these.

Solution

Question 9

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

$$(p\implies q)\vee(q\implies p)$$

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

$$(p\wedge q)\vee(q\wedge p)$$

Solution

Question 10

p is true, q is true.

p is false, q is false.

p is true, r is true.

Both (1) and (3)

Solution

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