Mathematical Reasoning CBSE Questions & Answers

Mathematical Reasoning

This is Mathematics Class 11 Mathematical Reasoning CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

Which of the following is a preposition?

A
Delhi is on the Jupiter
Correct
B
none of these
C
A half open door is half closed
D
I am an advocate

Let p and q be two prepositions given by P : The sky is blue, q : Milk is white, Then , p is

A
The sky is blue or milk is white
B
if the sky is blue then , milk is white
C
The sky is white and milk is blue
D
The sky is blue and milk is white
Correct

Let p and q be two prepositions given by p : I play cricket during the holidays, q : I just sleep throughout the day then , the compound statement p \( \wedge q\) is

A
I play cricket during the holidays or I just sleep throughout the day
Correct
B
I just sleep throughout the day if and only if I play cricket during the holidays
C
If I play cricket during the holidays , I just sleep throughout the day
D
I play cricket during the holidays and just sleep throughout the day

Let p and q be two prepositions given by p : It is hot, q : He wants water Then , the verbal meaning of \(p \to q\) is

A
it is hot and he wants water.
B
If it is hot , then he wants water.
Correct
C
it is hot or he wants water.
D
If and only if it is hot, he wants water.

Let p and q be two prepositions given by p : I take only bread and butter in breakfast. q : I do not take anything in breakfast. Then , the compound proposition “ I take only bread and butter in breakfast or I do not take anything “ is represented by

A
\(p \to q\)
B
p \( \vee q\)
Correct
C
p \( \vee q\)
D
\(p \leftrightarrow q\)

Let p and q be two prepositions given by p : I take medicine, q : I can sleep then ,the compound statement \( \sim p \sim q\) means

A
If I do not take medicine , then I can sleep.
B
I take medicine if I can sleep.
C
If I do not take medicine , then I cannot sleep.
Correct
D
I take medicine iff I can sleep.

Let p and q be two prepositions given by p : To become an airforce officer one should be graduate. q : To become an airforce officer one should have good health. The compound proposition “ To become an airforce officer one should be a graduate and should have good health “ is represented by

A
\(p \leftrightarrow q\)
B
\(p \to q\)
C
p \( \vee q\)
Correct
D
p \( \vee q\)

Let p and q be two prepositions given by p : A parallelogram is a rhombus. q : The diagonals are at right angles. The compound proposition “ A parallelogram is a rhombus iff its diagonals are at right angles “ is represented by

A
\(p \leftrightarrow q\)
Correct
B
p \( \vee q\)
C
p \( \vee q\)
D
\(p \to q\)

Let p and q be two prepositions given by p : I have the raincoat, q : I can walk in rain. The compound proposition “ If I have the raincoat , then I can walk in the rain “ is represented by

A
p \( \vee q\)
B
\( {\text{p}} \to {\text{q}}\)
Correct
C
\(p \leftrightarrow q\)
D
p \( \vee q\)

Which of the following is true for the propositions p and q ?

A
\(p \wedge q\) is true when atleast one of p and q is true.
B
\(p \leftrightarrow q\)is true only when both p and q are true
C
\( {\text{p}} \to {\text{q}}\) is true when p is true and q is false
D
\( \sim \left( {p \vee q} \right) \) is true only when both p and q are false.
Correct

The logically equivalent propositions of \(p \leftrightarrow q\) is

A
\((p \to q) \wedge (q \to p)\)
Correct
B
\((p \wedge q) \wedge (q \vee p)\)
C
\((p \to q) \vee (q \to p)\)
D
\((p \wedge q) \to (q \vee p)\)

\( \sim (p \vee q) \vee ( \sim p \wedge q)\) is logically equivalent to

A
\( \sim p\)
Correct
B
q
C
p
D
\( \sim q\)

If the inverse of implication \(p \to q\) is defined as \( \sim p \to \sim q\) , then the inverse of proposition \((p \wedge \sim q) \to r\) is

A
\(r \to p \wedge \sim q\)
B
none of these
C
\(( \sim p \vee q) \to \sim r\)
Correct
D
\( \sim r \to \sim p \vee q\)

Which of the following is logically equivalent to \((p \wedge q)\) ?

A
\(p \to \sim q\)
B
\( \sim (p \wedge \sim q)\)
C
\(( \sim p \wedge \sim q)\)
D
\( \sim ( \sim p \wedge \sim q)\)
Correct

Let p and q be two propositions. Then, the contrapositive of the implication \(p \to q\) is

A
\(p \to q\)
B
\(p \leftrightarrow q\)
C
\( \sim p \to \sim q\)
D
\( \sim q \to \sim p\)
Correct