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

1
Let p and q be two propositions. Then the implication \( \sim (p \leftrightarrow q)\) is :
  • A
    \(\left( {p \wedge \sim q} \right) \vee \left( { \sim p \wedge q} \right)\)
    Correct
  • B
    \( \sim p \vee \sim q\)
  • C
    none of these
  • D
    \( \sim p \wedge \sim q\)
2
\(p \wedge (q \wedge r)\) is logically equivalent to
  • A
    \((p \vee q) \vee r\)
  • B
    \((p \wedge q) \wedge r\)
    Correct
  • C
    \((p \vee q) \wedge r\)
  • D
    \(p \to (q \wedge r)\)
3
\( \sim ( \sim p) \leftrightarrow p\) is
  • A
    none of these
  • B
    neither a contradiction nor a tautology
  • C
    a contradiction
  • D
    a tautology
    Correct
4
Which of the following is a proposition ?
  • A
    I am a lion
  • B
    Logic is an interesting subject
  • C
    A triangle is a circle and 10 is a prime number
    Correct
  • D
    A half open door is half closed
5
Which of the following proposition is a tautology ?
  • A
    \(( \sim p \vee \sim q) \vee (p \vee \sim q)\)
    Correct
  • B
    \( \sim p \wedge ( \sim p \vee \sim q)\)
  • C
    \(( \sim p \vee \sim q) \wedge (p \vee \sim q)\)
  • D
    \( \sim q \wedge ( \sim p \vee \sim q)\)
6
Let p be the proposition : Mathematics is interesting and let q be the proposition that Mathematics is difficult, then the symbol \(p \wedge q\) means Mathematics is interesting and Mathematics is difficult
  • A
    Mathematics is interesting implies that Mathematics is difficult
  • B
    Mathematics is interesting implies and is implied by Mathematics is difficult
  • C
    Mathematics is interesting and Mathematics is difficult
    Correct
  • D
    Mathematics is interesting or Mathematics is difficult
7
The negation of the compound statement \(p \vee ( \sim p \vee q)\) is
  • A
    \((p \wedge \sim q) \vee \sim p\)
  • B
    \((p \wedge \sim q) \wedge \sim p\)
    Correct
  • C
    \((p \wedge \sim q) \vee p\)
  • D
    \((p \wedge q) \vee p\)
8
\( \sim (p \vee q) \vee ( \sim p \wedge q)\) is logically equivalent to
  • A
    q
  • B
    p
  • C
    \(\sim\)q
  • D
    \(\sim\)p
    Correct
9
The proposition \(p \to \sim (p \wedge \sim q)\) is
  • A
    a contradiction
  • B
    neither a contradiction nor a tautology
    Correct
  • C
    none of these
  • D
    a tautology
10
The proposition \((p \to \sim p) \wedge ( \sim p \to p)\) is
  • A
    a tautology
  • B
    a contradiction
    Correct
  • C
    neither a contradiction nor a tautology
  • D
    a contradiction and a tautology
11
The contrapositive of 2x + 3 = 9 \(x \ne \)4 is
  • A
    \(x \ne 4\), \(2x + 3 \ne 9\)
  • B
    x = 4, \(2x + 3 \ne \) 9
    Correct
  • C
    \(x \ne 42x + 3 = 9\)
  • D
    \(x = 4\),\( 2x + 3 = 9\)
12
Which of the following is equivalent to \((p \wedge q)\) ?
  • A
    \((p \to q)\)
  • B
    \( \sim (p \to \sim q)\)
    Correct
  • C
    \((p \wedge \sim q)\)
  • D
    \( \sim (p \to q)\)
13
Which of the following is logically equivalent to \( \sim ( \sim p \to q)\) ?
  • A
    \(( \sim p \wedge q)\)
  • B
    \(( \sim p \wedge \sim q)\)
    Correct
  • C
    \((p \vee \sim q)\)
  • D
    \((p \wedge q)\)
14
Which of the following is logically equivalent to \( \sim (p \leftrightarrow q)\) ?
  • A
    none of these
  • B
    \((p \vee q) \vee (q \wedge \sim p)\)
  • C
    \((p \vee \sim q) \vee (q \wedge \sim p)\)
    Correct
  • D
    \((p \vee q) \vee (q \wedge p)\)
15
\(p \to q\) is logically equivalent to
  • A
    \(p \wedge q\)
  • B
    \( \sim p \to \sim q\)
  • C
    \( \sim q \to \sim p\)
    Correct
  • D
    \(p \wedge \sim q\)